What is the extreme \sqrt[4]{x^4-81} ?

The extreme \sqrt[4]{x^4-81} is Minimum(-3,0),Minimum(3,0)

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extreme \sqrt[4]{x^4-81}

extreme

Minimum (- 3, 0), Minimum (3, 0)

Solution steps

f^{'} (x) = \frac{x ^{3}}{( x ^{4} - 81 ) ^{\frac{3}{4}}}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

4 x^{4} - 81 : 0

Minimum (- 3, 0)

Plug

x = 3

into

4 x^{4} - 81 : 0

Minimum (3, 0)

Minimum (- 3, 0), Minimum (3, 0)

What is the extreme \sqrt[4]{x^4-81} ?
The extreme \sqrt[4]{x^4-81} is Minimum(-3,0),Minimum(3,0)