What value of a and b has to take the function $x^3+ax^2+bx$ in order to have a minimum at $x=4$ and an inflection point at $x=1$?
I know that the derivative of the function is $3x^2+2xa+b$ but my problem here is that I don´t know how to establish the problem.
You are given that $f'(4)=0$ and $f''(1) = 0$. This gives you two equations for the two variables you want to solve for.