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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 1)

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = 1

into

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

Maximum (1, 1)

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

f (x) = x^{3} - 12 x^{2}

f (x) = 2 x^{3} + 3 x^{2} - 336 x

y = x^{4} + 6 x^{3} + 12 x^{2} + 8 x + 10

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

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

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