What is the extreme f(x)=x^{1/7}-x^{-6/7} ?

The extreme f(x)=x^{1/7}-x^{-6/7} is Maximum(-6,-6^{1/7}-1/((-6)^{6/7)})

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extreme f(x)=x^{1/7}-x^{-6/7}

extreme

Maximum (- 6, - 6^{\frac{1}{7}} - \frac{1}{( - 6 ) ^{\frac{6}{7}}})

Solution steps

Find the critical points:

x = - 6

Domain of

x^{\frac{1}{7}} - x^{- \frac{6}{7}} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = - 6

into

x^{\frac{1}{7}} - x^{- \frac{6}{7}} \Rightarrow y = - 6^{\frac{1}{7}} - \frac{1}{( - 6 ) ^{\frac{6}{7}}}

Maximum (- 6, - 6^{\frac{1}{7}} - \frac{1}{( - 6 ) ^{\frac{6}{7}}})

What is the extreme f(x)=x^{1/7}-x^{-6/7} ?
The extreme f(x)=x^{1/7}-x^{-6/7} is Maximum(-6,-6^{1/7}-1/((-6)^{6/7)})