What is the extreme f(x)=x^4-6x^2+4 ?

The extreme f(x)=x^4-6x^2+4 is Minimum(-sqrt(3),-5),Maximum(0,4),Minimum(sqrt(3),-5)

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extreme f(x)=x^4-6x^2+4

extreme points

f (x) = x^{4} - 6 x^{2} + 4

Minimum (- 3, - 5), Maximum (0, 4), Minimum (3, - 5)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x^{4} - 6 x^{2} + 4 : - 5

Minimum (- 3, - 5)

Plug

x = 0

into

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

Maximum (0, 4)

Plug

x = 3

into

x^{4} - 6 x^{2} + 4 : - 5

Minimum (3, - 5)

Minimum (- 3, - 5), Maximum (0, 4), Minimum (3, - 5)

f (x, y) = 3 x + y

f (x, y) = 6 - x^{4} + 2 x^{2} - y^{2}

4 x^{3} + 6 x + 2

f (x) = 5 x^{2} + 1, - 1 \leq x \leq 2

f (x) = - 3 x^{2} y - 84 x y + 7 y^{2}

What is the extreme f(x)=x^4-6x^2+4 ?
The extreme f(x)=x^4-6x^2+4 is Minimum(-sqrt(3),-5),Maximum(0,4),Minimum(sqrt(3),-5)