What is the extreme f(x)=2x^2-2x^4 ?

The extreme f(x)=2x^2-2x^4 is Maximum(-1/(sqrt(2)), 1/2),Minimum(0,0),Maximum(1/(sqrt(2)), 1/2)

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extreme f(x)=2x^2-2x^4

extreme points

f (x) = 2 x^{2} - 2 x^{4}

Maximum (- \frac{1}{2}, \frac{1}{2}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{2})

Solution steps

f^{'} (x) = 4 x - 8 x^{3}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0,

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

2 x^{2} - 2 x^{4} : \frac{1}{2}

Maximum (- \frac{1}{2}, \frac{1}{2})

Plug

x = 0

into

2 x^{2} - 2 x^{4} : 0

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

2 x^{2} - 2 x^{4} : \frac{1}{2}

Maximum (\frac{1}{2}, \frac{1}{2})

Maximum (- \frac{1}{2}, \frac{1}{2}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{2})

f (x) = 2 e^{x^{2} - 2 x + 1}

f (x, y) = 6 x^{2} + 2 y^{2}

f (x) = \frac{2 x - 5}{x}

\frac{5}{x + 6}

f (x) = x^{5} - 5 x^{4} - x^{3} + 28 x^{2} - 2 x

What is the extreme f(x)=2x^2-2x^4 ?
The extreme f(x)=2x^2-2x^4 is Maximum(-1/(sqrt(2)), 1/2),Minimum(0,0),Maximum(1/(sqrt(2)), 1/2)