What is the extreme f(x)=-x^4+4x^2+3 ?

The extreme f(x)=-x^4+4x^2+3 is Maximum(-sqrt(2),7),Minimum(0,3),Maximum(sqrt(2),7)

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extreme f(x)=-x^4+4x^2+3

extreme points

f (x) = - x^{4} + 4 x^{2} + 3

Maximum (- 2, 7), Minimum (0, 3), Maximum (2, 7)

Solution steps

f^{'} (x) = - 4 x^{3} + 8 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} + 4 x^{2} + 3 : 7

Maximum (- 2, 7)

Plug

x = 0

into

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

Minimum (0, 3)

Plug

x = 2

into

- x^{4} + 4 x^{2} + 3 : 7

Maximum (2, 7)

Maximum (- 2, 7), Minimum (0, 3), Maximum (2, 7)

f (x) = 10 (x + 7)

(- 3, 2), (7, - 3)

y = - 2 x - 1

\frac{x + 2}{6}

f (x) = x + 4, x < 1

What is the extreme f(x)=-x^4+4x^2+3 ?
The extreme f(x)=-x^4+4x^2+3 is Maximum(-sqrt(2),7),Minimum(0,3),Maximum(sqrt(2),7)