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

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

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

extreme points

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

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 1)

Maximum (- 1, 1), Minimum (0, 0), Maximum (1, 1)

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

f (x, y) = x + y

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

f (x, y) = e^{x y}

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

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