How to find the first root of a function with 1 variable?

Question

I have a function with 1 variable x (positive number), I want to find the smallest root (the smallest x, where f(x)=0), I know that my root is bigger than 6.5. and I have graphed the function for value of x=6.5 to x=6.55 function's graph for value of x=6.5 to x=6.55 this is my function: (e is exponent)

f=(3.0*(6.7e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-6.7e-3*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-1.7e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(100.0*cos(1000*x)^2+1.5e3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)^2+(2.8e-3*cos(1000*x)-2.8)^2+(18.0*cos(1000*x)+0.018)*(2.8*cos(1000*x)+2.8e-3)+(0.018*cos(1000*x)+18.0)*(2.8e-3*cos(1000*x)+2.8))-0.042*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+6.7e-3*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+0.042*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2+1.7e-3*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+0.042*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))-1.7e-3*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2+1.3*sin(1000*x)^2*(x-8.0)^2)^2-1.0*(0.02*((1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))-71.0*sin(1000*x)*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3))*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))+0.01*((x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+32.0*sin(1000*x)^2*(x-8.0)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))+0.01*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(4.0*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+25.0*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2)+0.01*((x-8.0)*(4.0*x-32.0)-1.0)*(4.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-(25.0*cos(1000*x)^2+366.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+25.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2-(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2-(4.0*cos(1000*x)^2+58.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)))+0.01*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))*((cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-1.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2+(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+200.0*sin(1000*x)^2*(x-8.0)^2)-0.02*(x-8.0)*(2.8e-3*cos(1000*x)-2.8)*((x-8.0)*(2.8*cos(1000*x)+2.8e-3)*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))+2.8*sin(1000*x)*(x-8.0)*(11.0*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+71.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-4.0e-3*cos(1000*x)*sin(1000*x))))*(0.25*cos(1000*x)^2+3.7*sin(1000*x)^2-0.25*(x-8.0)*(4.0*x-32.0)+0.062*(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+0.01*(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+0.01*(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)+0.062*(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3)+0.25)+1.0)^3-27.0*(6.7e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-6.7e-3*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-1.7e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(100.0*cos(1000*x)^2+1.5e3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)^2+(2.8e-3*cos(1000*x)-2.8)^2+(18.0*cos(1000*x)+0.018)*(2.8*cos(1000*x)+2.8e-3)+(0.018*cos(1000*x)+18.0)*(2.8e-3*cos(1000*x)+2.8))-0.042*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+6.7e-3*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+0.042*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2+1.7e-3*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+0.042*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))-(5.0e-3*((1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))-71.0*sin(1000*x)*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3))*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))+2.5e-3*((x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+32.0*sin(1000*x)^2*(x-8.0)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))+2.5e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(4.0*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+25.0*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2)+2.5e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(4.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-(25.0*cos(1000*x)^2+366.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+25.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2-(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2-(4.0*cos(1000*x)^2+58.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)))+2.5e-3*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))*((cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-1.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2+(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+200.0*sin(1000*x)^2*(x-8.0)^2)-5.0e-3*(x-8.0)*(2.8e-3*cos(1000*x)-2.8)*((x-8.0)*(2.8*cos(1000*x)+2.8e-3)*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))+2.8*sin(1000*x)*(x-8.0)*(11.0*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+71.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-4.0e-3*cos(1000*x)*sin(1000*x))))*(5.0e-3*((1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))-71.0*sin(1000*x)*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3))*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))-1.0*(0.25*cos(1000*x)^2+3.7*sin(1000*x)^2-0.25*(x-8.0)*(4.0*x-32.0)+0.062*(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+0.01*(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+0.01*(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)+0.062*(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3)+0.25)*(6.7e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-6.7e-3*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-1.7e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(100.0*cos(1000*x)^2+1.5e3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)^2+(2.8e-3*cos(1000*x)-2.8)^2+(18.0*cos(1000*x)+0.018)*(2.8*cos(1000*x)+2.8e-3)+(0.018*cos(1000*x)+18.0)*(2.8e-3*cos(1000*x)+2.8))-0.042*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+6.7e-3*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+0.042*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2+1.7e-3*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+0.042*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))-1.7e-3*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2+1.3*sin(1000*x)^2*(x-8.0)^2)+2.5e-3*((x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+32.0*sin(1000*x)^2*(x-8.0)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))+2.5e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(4.0*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+25.0*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2)+2.5e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(4.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-(25.0*cos(1000*x)^2+366.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+25.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2-(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2-(4.0*cos(1000*x)^2+58.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)))+2.5e-3*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))*((cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-1.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2+(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+200.0*sin(1000*x)^2*(x-8.0)^2)-5.0e-3*(x-8.0)*(2.8e-3*cos(1000*x)-2.8)*((x-8.0)*(2.8*cos(1000*x)+2.8e-3)*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))+2.8*sin(1000*x)*(x-8.0)*(11.0*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+71.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-4.0e-3*cos(1000*x)*sin(1000*x))))+(1.0*(5.0e-3*((1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))-71.0*sin(1000*x)*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3))*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))+2.5e-3*((x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+32.0*sin(1000*x)^2*(x-8.0)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))+2.5e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(4.0*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+25.0*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2-1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2)+2.5e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(4.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-(25.0*cos(1000*x)^2+366.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+25.0*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2-(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+1.0*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2-(4.0*cos(1000*x)^2+58.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)))+2.5e-3*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))*((cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-1.0*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2+(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+200.0*sin(1000*x)^2*(x-8.0)^2)-5.0e-3*(x-8.0)*(2.8e-3*cos(1000*x)-2.8)*((x-8.0)*(2.8*cos(1000*x)+2.8e-3)*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))+2.8*sin(1000*x)*(x-8.0)*(11.0*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+71.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-4.0e-3*cos(1000*x)*sin(1000*x))))*(0.25*cos(1000*x)^2+3.7*sin(1000*x)^2-0.25*(x-8.0)*(4.0*x-32.0)+0.062*(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+0.01*(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+0.01*(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)+0.062*(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3)+0.25)-(6.7e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-6.7e-3*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-1.7e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(100.0*cos(1000*x)^2+1.5e3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)^2+(2.8e-3*cos(1000*x)-2.8)^2+(18.0*cos(1000*x)+0.018)*(2.8*cos(1000*x)+2.8e-3)+(0.018*cos(1000*x)+18.0)*(2.8e-3*cos(1000*x)+2.8))-0.042*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+6.7e-3*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+0.042*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2+1.7e-3*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+0.042*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))-1.7e-3*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2+1.3*sin(1000*x)^2*(x-8.0)^2)^2)*(6.7e-3*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))-6.7e-3*(2.8*sin(1000*x)*(7.1e-4*cos(1000*x)-0.71)+18.0*sin(1000*x)*(7.1e-4*cos(1000*x)+0.71)-1.0e-3*cos(1000*x)*sin(1000*x))^2-1.7e-3*((x-8.0)*(4.0*x-32.0)-1.0)*(100.0*cos(1000*x)^2+1.5e3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)^2+(2.8e-3*cos(1000*x)-2.8)^2+(18.0*cos(1000*x)+0.018)*(2.8*cos(1000*x)+2.8e-3)+(0.018*cos(1000*x)+18.0)*(2.8e-3*cos(1000*x)+2.8))-0.042*(0.71*sin(1000*x)*(18.0*cos(1000*x)-0.018)+0.71*sin(1000*x)*(2.8*cos(1000*x)+2.8e-3)-1.0*cos(1000*x)*sin(1000*x))^2+6.7e-3*(x-8.0)^2*(2.8e-3*cos(1000*x)-2.8)^2+0.042*(x-8.0)^2*(2.8*cos(1000*x)+2.8e-3)^2+1.7e-3*(1.0e-6*sin(1000*x)^2+(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8))*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))+0.042*(cos(1000*x)^2+15.0*sin(1000*x)^2)*(1.0*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3))-1.7e-3*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2+1.3*sin(1000*x)^2*(x-8.0)^2)-(0.25*cos(1000*x)^2+3.7*sin(1000*x)^2-0.25*(x-8.0)*(4.0*x-32.0)+0.062*(18.0*cos(1000*x)-0.018)*(0.71*cos(1000*x)-7.1e-4)+0.01*(0.018*cos(1000*x)+18.0)*(7.1e-4*cos(1000*x)+0.71)+0.01*(7.1e-4*cos(1000*x)-0.71)*(2.8e-3*cos(1000*x)-2.8)+0.062*(0.71*cos(1000*x)+7.1e-4)*(2.8*cos(1000*x)+2.8e-3)+0.25)^2-1.7e-3*(1.0e-3*sin(1000*x)^2+(18.0*cos(1000*x)-0.018)*(7.1e-4*cos(1000*x)+0.71)+(7.1e-4*cos(1000*x)-0.71)*(2.8*cos(1000*x)+2.8e-3))^2+1.3*sin(1000*x)^2*(x-8.0)^2)^2

if you do it manually you will find out that the solution for this problem is solution

But I need a more general solution as my goal is to find the first root of this function when you replace each (1000*x) in the function with (x*10^15)

Answer 1

In general, there is no single algorithm to find the root of a function, and the algorithm needed will be context dependent. Algorithms used for finding the roots of functions are called root finding algorithms.

Label the root $\alpha$. Since $f(x)$ is continuous, we can find an interval for $\alpha$ by finding where $f(x)$ changes sign.

We could find the first $n\in\mathbb{N}$, for small enough $\Delta x$, such that $f(n\Delta x)<0$. This method isn't very efficient (less than the method of bisection) but it can give us an interval that contains $\alpha$. Also, if $f(x)$ oscillates rapidly, to the point where it's almost discontinuous, this method might be more appropriate. For $\Delta x=1$, the method tells us that $f(8)$ is the first $f(x)<0$. Hence, $\alpha\approx8$, or $\alpha\in(7,8)$. This doesn't actually prove that the lowest root is in this interval, it's just the lowest root we know of. This method is in the Python3 code below.

x=0
h=1        #partition width
bound=10        #highest value of x we'll check
while x<bound:
    if f(x)<0:
        print(x)
        x=bound
    else:
        x=x+h

A simple root finding algorithm is the method of bisection. This method splits the interval in half, depending on the sign of the function at the midpoint. If the original interval is $(a,b)$, the new interval is $(a,\frac{a+b}{2})$ if $f\left(\frac{a+b}{2}\right)$ has the opposite sign to $f(a)$ or $(\frac{a+b}{2},b)$, if not. The Python3 code below tells us, for enough iterations, that $\alpha=7.207343999412696\pm10^{-15}$. You could do the same method with $\cos(x\cdot10^{15})$ in your function too but it would oscillate so quickly, it might be tricky to know if your root is really the first root.

a=7        #lower bound of interval
b=8        #upper bound
n=10        #number of iterations
i=0        #index of iterations
while i<n:
    if f((a+b)/2)<0:
        b=(a+b)/2
        print(a,b)
        i=i+1
    else:
        a=(a+b)/2
        print(a,b)
        i=i+1

There are other algorithms that can be used, but they depend on the degree of continuity and differentiability of the function in question. Your function oscillates fairly rapidly, so methods like the secant method or Newton-Raphson method might fail. The figure below shows a GNUPLOT graph of $f(x)$ over $(5,8)$.