What is the extreme f(x)=2x^3+4x^2-8x-11 ?

The extreme f(x)=2x^3+4x^2-8x-11 is Maximum(-2,5),Minimum(2/3 ,-377/27)

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extreme f(x)=2x^3+4x^2-8x-11

extreme points

f (x) = 2 x^{3} + 4 x^{2} - 8 x - 11

Maximum (- 2, 5), Minimum (\frac{2}{3}, - \frac{377}{27})

Solution steps

f^{'} (x) = 6 x^{2} + 8 x - 8

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

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

Increasing

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

Plug

x = - 2

into

2 x^{3} + 4 x^{2} - 8 x - 11 : 5

Maximum (- 2, 5)

Plug

x = \frac{2}{3}

into

2 x^{3} + 4 x^{2} - 8 x - 11 : - \frac{377}{27}

Minimum (\frac{2}{3}, - \frac{377}{27})

Maximum (- 2, 5), Minimum (\frac{2}{3}, - \frac{377}{27})

\frac{3}{4 \frac{5 + 3 x}{2}}

5 sin (6 x - π)

\frac{2}{( x + 1 ) ^{3}}

(3, 10), (- 2, - 2)

\frac{cos ( x )}{( sin ( x ) ) ^{0.5}}

What is the extreme f(x)=2x^3+4x^2-8x-11 ?
The extreme f(x)=2x^3+4x^2-8x-11 is Maximum(-2,5),Minimum(2/3 ,-377/27)