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

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

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extreme x^4-2x^2-2

extreme points

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

Minimum (- 1, - 3), Maximum (0, - 2), 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} - 2 : - 3

Minimum (- 1, - 3)

Plug

x = 0

into

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

Maximum (0, - 2)

Plug

x = 1

into

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

Minimum (1, - 3)

Minimum (- 1, - 3), Maximum (0, - 2), Minimum (1, - 3)

x^{4} - 2 x^{2} + 1

y = 63 x + 12 cos (x)

f (x, y) = x^{2} + 7 y^{2} + x - 6 y + 4

f (x) = 2 x^{2} ln (x) - 19 x^{2}

f (x, y) = x^{2} + 9 x y + y^{2}

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