Question

What are the critical values, if any, of `f(x)= 3x^3+7x^2-8x`?

Answer 1

Local maximum with concave down @ x = -2 & local minimum with concave up @ x = 4/9.

Explanation:

`f’(x)=9x^2+14x-8`
`9x^2+14x-8=0`
`9x^2+18x-4x-8=0`
#9x((x+2)-4(x+2)=0 #x=-2, 4/9#

`f”(x)=18x+14`
`f”(-2)=-36+14=-22`
`f”(4/9)=16+14=30`

Local maximum with concave down @ x = -2 & local minimum with concave up @ x = 4/9.