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

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

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

extreme points

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

Maximum (- \frac{1}{2}, \frac{1}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4})

Solution steps

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

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

Maximum (- \frac{1}{2}, \frac{1}{4})

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, \frac{1}{4})

Maximum (- \frac{1}{2}, \frac{1}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4})

f (x, y) = 5 - x^{2} - y^{2}

f (x, y) = x^{3} + y^{3} + 3 x y

f (x, y) = 2 x^{2} + 3 y^{2} - 12 x - 2 y + 1

x^{2} (x - 1) (2 x + 1) + y^{2}

f (x, y) = \frac{x y}{x ^{2} + y ^{2} - 25}

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