What is the extreme x^4-4x^2+2 ?

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

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extreme x^4-4x^2+2

extreme points

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

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

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} + 2 : - 2

Minimum (- 2, - 2)

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = 2

into

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

Minimum (2, - 2)

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

(x^{2} - 4)^{7}

f (x, y) = \frac{1}{16 - 4 x ^{2} - y ^{2}}

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

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

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

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