Given that f(x)=x^3+ax^2+bx has critical points at x=1 and x=5, find a and b and classify the critical points as maxima, minima, or neither.

Answer 1

f' = 3x^2+2ax+b

Now just find a and b so that f' has factors (x-1)(x-5)

Then you can determine the rest using f".