What is the extreme (x^2-9)^6 ?

The extreme (x^2-9)^6 is Minimum(-3,0),Maximum(0,531441),Minimum(3,0)

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extreme (x^2-9)^6

extreme

Minimum (- 3, 0), Maximum (0, 531441), Minimum (3, 0)

Solution steps

f^{'} (x) = 12 x (x^{2} - 9)^{5}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

(x^{2} - 9)^{6} : 0

Minimum (- 3, 0)

Plug

x = 0

into

(x^{2} - 9)^{6} : 531441

Maximum (0, 531441)

Plug

x = 3

into

(x^{2} - 9)^{6} : 0

Minimum (3, 0)

Minimum (- 3, 0), Maximum (0, 531441), Minimum (3, 0)

What is the extreme (x^2-9)^6 ?
The extreme (x^2-9)^6 is Minimum(-3,0),Maximum(0,531441),Minimum(3,0)