What is the extreme f(x)=-5x^6ln(x),(0,4) ?

The extreme f(x)=-5x^6ln(x),(0,4) is Maximum(1/(\sqrt[6]{e)}, 5/(6e))

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extreme f(x)=-5x^6ln(x),(0,4)

extreme

Maximum (\frac{1}{6 e}, \frac{5}{6 e})

Solution steps

Find the critical points:

x = \frac{1}{6 e}

Domain of

- 5 x^{6} ln (x), (0, 4) : 0 < x < 4

Find intervals:

Increasing

: 0 < x < \frac{1}{6 e},

Decreasing

: \frac{1}{6 e} < x < 4

Plug the extreme point

x = \frac{1}{6 e}

into

- 5 x^{6} ln (x) \Rightarrow y = \frac{5}{6 e}

Maximum (\frac{1}{6 e}, \frac{5}{6 e})

What is the extreme f(x)=-5x^6ln(x),(0,4) ?
The extreme f(x)=-5x^6ln(x),(0,4) is Maximum(1/(\sqrt[6]{e)}, 5/(6e))