What is the extreme f(x)=x^4-4x^2+10 ?

The extreme f(x)=x^4-4x^2+10 is Minimum(-sqrt(2),6),Maximum(0,10),Minimum(sqrt(2),6)

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extreme f(x)=x^4-4x^2+10

extreme points

f (x) = x^{4} - 4 x^{2} + 10

Minimum (- 2, 6), Maximum (0, 10), Minimum (2, 6)

Solution steps

f^{'} (x) = 4 x^{3} - 8 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x^{4} - 4 x^{2} + 10 : 6

Minimum (- 2, 6)

Plug

x = 0

into

x^{4} - 4 x^{2} + 10 : 10

Maximum (0, 10)

Plug

x = 2

into

x^{4} - 4 x^{2} + 10 : 6

Minimum (2, 6)

Minimum (- 2, 6), Maximum (0, 10), Minimum (2, 6)

f (x) = x^{3} - 12 x^{2} + 21 x + 1

y = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

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

f (x) = - 28 x^{2} + 311 x

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

What is the extreme f(x)=x^4-4x^2+10 ?
The extreme f(x)=x^4-4x^2+10 is Minimum(-sqrt(2),6),Maximum(0,10),Minimum(sqrt(2),6)