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

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

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extreme f(x)=-5x^6ln(x)

extreme

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

Solution steps

f^{'} (x) = - 5 (6 x^{5} ln (x) + x^{5})

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{1}{6 e}

into

- 5 x^{6} ln (x) : \frac{5}{6 e}

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

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