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

The extreme f(x)=-x^4+8x^2+6 is Maximum(-2,22),Minimum(0,6),Maximum(2,22)

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

extreme points

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

Maximum (- 2, 22), Minimum (0, 6), Maximum (2, 22)

Solution steps

f^{'} (x) = - 4 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

- x^{4} + 8 x^{2} + 6 : 22

Maximum (- 2, 22)

Plug

x = 0

into

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

Minimum (0, 6)

Plug

x = 2

into

- x^{4} + 8 x^{2} + 6 : 22

Maximum (2, 22)

Maximum (- 2, 22), Minimum (0, 6), Maximum (2, 22)

What is the extreme f(x)=-x^4+8x^2+6 ?
The extreme f(x)=-x^4+8x^2+6 is Maximum(-2,22),Minimum(0,6),Maximum(2,22)