What is the extreme (x^2+12)(144-x^2) ?

The extreme (x^2+12)(144-x^2) is Maximum(-sqrt(66),6084),Minimum(0,1728),Maximum(sqrt(66),6084)

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extreme (x^2+12)(144-x^2)

extreme

Maximum (- 66, 6084), Minimum (0, 1728), Maximum (66, 6084)

Solution steps

f^{'} (x) = - 4 x (x + 66) (x - 66)

Find intervals:

Increasing

: - \infty < x < - 66,

Decreasing

: - 66 < x < 0,

Increasing

: 0 < x < 66,

Decreasing

: 66 < x < \infty

Plug

x = - 66

into

(x^{2} + 12) (144 - x^{2}) : 6084

Maximum (- 66, 6084)

Plug

x = 0

into

(x^{2} + 12) (144 - x^{2}) : 1728

Minimum (0, 1728)

Plug

x = 66

into

(x^{2} + 12) (144 - x^{2}) : 6084

Maximum (66, 6084)

Maximum (- 66, 6084), Minimum (0, 1728), Maximum (66, 6084)

What is the extreme (x^2+12)(144-x^2) ?
The extreme (x^2+12)(144-x^2) is Maximum(-sqrt(66),6084),Minimum(0,1728),Maximum(sqrt(66),6084)