What is the extreme x^3+2x^2-4x-8 ?

The extreme x^3+2x^2-4x-8 is Maximum(-2,0),Minimum(2/3 ,-256/27)

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extreme x^3+2x^2-4x-8

extreme points

x^{3} + 2 x^{2} - 4 x - 8

Maximum (- 2, 0), Minimum (\frac{2}{3}, - \frac{256}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 4 x - 4

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - 2

into

x^{3} + 2 x^{2} - 4 x - 8 : 0

Maximum (- 2, 0)

Plug

x = \frac{2}{3}

into

x^{3} + 2 x^{2} - 4 x - 8 : - \frac{256}{27}

Minimum (\frac{2}{3}, - \frac{256}{27})

Maximum (- 2, 0), Minimum (\frac{2}{3}, - \frac{256}{27})

f (x) = 2 x^{2} - 100 ln (x)

x^{3} - 4 x

\frac{x}{x ^{2} + 16 x + 60}

∣ sin (x) ∣

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 4

What is the extreme x^3+2x^2-4x-8 ?
The extreme x^3+2x^2-4x-8 is Maximum(-2,0),Minimum(2/3 ,-256/27)