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

The extreme f(x)=2x^3+2x^2-2x is Maximum(-1,2),Minimum(1/3 ,-10/27)

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

extreme points

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

Maximum (- 1, 2), Minimum (\frac{1}{3}, - \frac{10}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - 1

into

2 x^{3} + 2 x^{2} - 2 x : 2

Maximum (- 1, 2)

Plug

x = \frac{1}{3}

into

2 x^{3} + 2 x^{2} - 2 x : - \frac{10}{27}

Minimum (\frac{1}{3}, - \frac{10}{27})

Maximum (- 1, 2), Minimum (\frac{1}{3}, - \frac{10}{27})

y = \frac{2 x}{x ^{2} + 49}

f (x) = 4 x^{3} - 6 x^{2} + 3 x - 1

f (x) = \frac{( 7 x + 1 )}{x - 3}

y = - \frac{4}{5} x + 4

f (x) = \frac{( \frac{x}{5} )}{( \frac{x}{5} ) + 5}

What is the extreme f(x)=2x^3+2x^2-2x ?
The extreme f(x)=2x^3+2x^2-2x is Maximum(-1,2),Minimum(1/3 ,-10/27)