I have the following problem.
Determine the equation of the tangent to the curve defined by $f(x)=x^2-6x+14$ at the point $(1,9)$, and then sketch it.
I'm having trouble with this question as I have no lessons whatsoever on it, the only example is telling me to complete the square to sketch it, and its not working out when I try that. Any help would be appreciated.
Take the derivative of $f(x): f'(x)=2x-6.$ So we have that the slope is $m=f'(1)=-4.$ Now, the equation of the tangent is $y=9+(-4)(x-1)=-4x+13.$