Question

Find the extreme point(s) of the function f(x) = 0.25x^4+3x^3-18x^2+10 and classify them.

Answer 1

1 - Differentiate f(x)
2 - Solve f'(x)=0
3 - Use sign diagram or 2nd derivative for classification of the extreme points

---I'll do 1 and 2 for you... ---

1: f'(x)=x^3+9x^2-36x

2: Solution by factorization: x(x^2+9x-36)=0 , x(x+12)(x-3)=0
solutions: x=0, x=-12, x=3

3: f''(x)=3x^2+18x-36
f''(0)=-36<0 -> Local max at x=0 Point (0,10)
f''(-12) (saved as exercise ;-) ...
f''(3)...

Answer 2

Thanks for your help. I will finish it.