Question

Is this correct? (Calculus)

Use the second derivative test to find all relative extrema of f(x)= 5 + 3x^2-x^3

f'(x)=-3(x-2)x
f"(x)=6-6x

critical value: -6?

minima= x=-6
no maxima?

Answer 1

in x=o f''(0)=6 minima
in x=2 f''(2)=6-12<0 so it is maximum