What is the extreme f(x)=x^{15/7}-x^{8/7} ?

The extreme f(x)=x^{15/7}-x^{8/7} is Maximum(0,0),Minimum(8/15 ,(8/15)^{15/7}-(8/15)^{8/7})

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extreme f(x)=x^{15/7}-x^{8/7}

extreme

Maximum (0, 0), Minimum (\frac{8}{15}, (\frac{8}{15})^{\frac{15}{7}} - (\frac{8}{15})^{\frac{8}{7}})

Solution steps

Find the critical points:

x = 0, x = \frac{8}{15}

Domain of

x^{\frac{15}{7}} - x^{\frac{8}{7}} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{8}{15},

Increasing

: \frac{8}{15} < x < \infty

Plug the extreme point

x = 0

into

x^{\frac{15}{7}} - x^{\frac{8}{7}} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = \frac{8}{15}

into

x^{\frac{15}{7}} - x^{\frac{8}{7}} \Rightarrow y = (\frac{8}{15})^{\frac{15}{7}} - (\frac{8}{15})^{\frac{8}{7}}

Minimum (\frac{8}{15}, (\frac{8}{15})^{\frac{15}{7}} - (\frac{8}{15})^{\frac{8}{7}})

Maximum (0, 0), Minimum (\frac{8}{15}, (\frac{8}{15})^{\frac{15}{7}} - (\frac{8}{15})^{\frac{8}{7}})

What is the extreme f(x)=x^{15/7}-x^{8/7} ?
The extreme f(x)=x^{15/7}-x^{8/7} is Maximum(0,0),Minimum(8/15 ,(8/15)^{15/7}-(8/15)^{8/7})