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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

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

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

Plug

x = 1

into

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

Maximum (1, 2)

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

\frac{sin ( x )}{x}

2 x^{3} - 4 x^{2} - 10 x + 20

f (x) = x 8 - x

f (x) = - 6 x^{2} + 12000 x

(x - 5)^{2} - 4

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