What is the extreme f(x)=-x^4+2x^2+1 ?

The extreme f(x)=-x^4+2x^2+1 is Maximum(-1,2),Minimum(0,1),Maximum(1,2)

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extreme f(x)=-x^4+2x^2+1

extreme points

f (x) = - x^{4} + 2 x^{2} + 1

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 2)

Plug

x = 0

into

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

Minimum (0, 1)

Plug

x = 1

into

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

Maximum (1, 2)

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

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