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

Oct 12, 2017

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

#### Explanation:

f’(x)=9x^2+14x-8
$9 {x}^{2} + 14 x - 8 = 0$
$9 {x}^{2} + 18 x - 4 x - 8 = 0$
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.