What is the extreme f(x)=-2/3 x^3+2x^2+6x+6 ?

The extreme f(x)=-2/3 x^3+2x^2+6x+6 is Minimum(-1, 8/3),Maximum(3,24)

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extreme f(x)=-2/3 x^3+2x^2+6x+6

extreme points

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6

Minimum (- 1, \frac{8}{3}), Maximum (3, 24)

Solution steps

f^{'} (x) = - 2 x^{2} + 4 x + 6

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6 : \frac{8}{3}

Minimum (- 1, \frac{8}{3})

Plug

x = 3

into

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6 : 24

Maximum (3, 24)

Minimum (- 1, \frac{8}{3}), Maximum (3, 24)

What is the extreme f(x)=-2/3 x^3+2x^2+6x+6 ?
The extreme f(x)=-2/3 x^3+2x^2+6x+6 is Minimum(-1, 8/3),Maximum(3,24)