What is the extreme 5+4x^2-x^4 ?

The extreme 5+4x^2-x^4 is Maximum(-sqrt(2),9),Minimum(0,5),Maximum(sqrt(2),9)

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extreme 5+4x^2-x^4

extreme points

5 + 4 x^{2} - x^{4}

Maximum (- 2, 9), Minimum (0, 5), Maximum (2, 9)

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

5 + 4 x^{2} - x^{4} : 9

Maximum (- 2, 9)

Plug

x = 0

into

5 + 4 x^{2} - x^{4} : 5

Minimum (0, 5)

Plug

x = 2

into

5 + 4 x^{2} - x^{4} : 9

Maximum (2, 9)

Maximum (- 2, 9), Minimum (0, 5), Maximum (2, 9)

f (x) = x^{2} + 3, - 1 \leq x \leq 4

f (x, y) = 5 x + 5 y

f (x) = \frac{1}{4} (- 4 x^{3} + 2 x^{2} + 12)

f (x, y) = x^{2} - 2 y^{2} + 8 x - 3 y + 1

f (2) = \frac{x}{e ^{- x}}

What is the extreme 5+4x^2-x^4 ?
The extreme 5+4x^2-x^4 is Maximum(-sqrt(2),9),Minimum(0,5),Maximum(sqrt(2),9)