What is the extreme 7+4x^2-x^4 ?

The extreme 7+4x^2-x^4 is Maximum(-sqrt(2),11),Minimum(0,7),Maximum(sqrt(2),11)

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extreme 7+4x^2-x^4

extreme

Maximum (- 2, 11), Minimum (0, 7), Maximum (2, 11)

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

7 + 4 x^{2} - x^{4} : 11

Maximum (- 2, 11)

Plug

x = 0

into

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

Minimum (0, 7)

Plug

x = 2

into

7 + 4 x^{2} - x^{4} : 11

Maximum (2, 11)

Maximum (- 2, 11), Minimum (0, 7), Maximum (2, 11)

What is the extreme 7+4x^2-x^4 ?
The extreme 7+4x^2-x^4 is Maximum(-sqrt(2),11),Minimum(0,7),Maximum(sqrt(2),11)