What is the extreme f(x)=-2x^4+8x^2-6 ?

The extreme f(x)=-2x^4+8x^2-6 is Maximum(-sqrt(2),2),Minimum(0,-6),Maximum(sqrt(2),2)

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extreme f(x)=-2x^4+8x^2-6

extreme points

f (x) = - 2 x^{4} + 8 x^{2} - 6

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

Solution steps

f^{'} (x) = - 8 x^{3} + 16 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- 2 x^{4} + 8 x^{2} - 6 : 2

Maximum (- 2, 2)

Plug

x = 0

into

- 2 x^{4} + 8 x^{2} - 6 : - 6

Minimum (0, - 6)

Plug

x = 2

into

- 2 x^{4} + 8 x^{2} - 6 : 2

Maximum (2, 2)

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

d o main f (x) = ∣ x ∣ - 2

mi d p o in t (- 7, - 4), (1, - 8)

d o main f (x) = \frac{1}{2 9 - x}

d o main f (x) = x^{2} + y^{2} = 4

s l o p e 11 x + 6 y = 3

What is the extreme f(x)=-2x^4+8x^2-6 ?
The extreme f(x)=-2x^4+8x^2-6 is Maximum(-sqrt(2),2),Minimum(0,-6),Maximum(sqrt(2),2)