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

The extreme f(x)=x^4-2x^2+4 is Minimum(-1,3),Maximum(0,4),Minimum(1,3)

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

extreme points

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

Minimum (- 1, 3), Maximum (0, 4), Minimum (1, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{4} - 2 x^{2} + 4 : 3

Minimum (- 1, 3)

Plug

x = 0

into

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

Maximum (0, 4)

Plug

x = 1

into

x^{4} - 2 x^{2} + 4 : 3

Minimum (1, 3)

Minimum (- 1, 3), Maximum (0, 4), Minimum (1, 3)

y = \frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + 8

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

y = (x^{2} - 9)^{4}

f (x) = \frac{3 x}{x ^{2} - 4}

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

What is the extreme f(x)=x^4-2x^2+4 ?
The extreme f(x)=x^4-2x^2+4 is Minimum(-1,3),Maximum(0,4),Minimum(1,3)