What is the extreme f(x)=x^4-2x^2+5 ?

The extreme f(x)=x^4-2x^2+5 is Minimum(-1,4),Maximum(0,5),Minimum(1,4)

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extreme f(x)=x^4-2x^2+5

extreme points

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

Minimum (- 1, 4), Maximum (0, 5), Minimum (1, 4)

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} + 5 : 4

Minimum (- 1, 4)

Plug

x = 0

into

x^{4} - 2 x^{2} + 5 : 5

Maximum (0, 5)

Plug

x = 1

into

x^{4} - 2 x^{2} + 5 : 4

Minimum (1, 4)

Minimum (- 1, 4), Maximum (0, 5), Minimum (1, 4)

f (x) = 4 x^{2} - 4 x + 1

y = x^{3} - 3 x^{2}

f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15

f (x) = x^{3} - 3 x^{2} + 6

f (x, y) = x^{2} + y^{2} - 2 x - 6 y + 14

What is the extreme f(x)=x^4-2x^2+5 ?
The extreme f(x)=x^4-2x^2+5 is Minimum(-1,4),Maximum(0,5),Minimum(1,4)