What is the extreme f(x)=-3x^6ln(2x) ?

The extreme f(x)=-3x^6ln(2x) is Maximum(1/(2\sqrt[6]{e)}, 1/(128e))

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extreme f(x)=-3x^6ln(2x)

extreme

Maximum (\frac{1}{2 6 e}, \frac{1}{128 e})

Solution steps

f^{'} (x) = - 3 (6 x^{5} ln (2 x) + x^{5})

Find intervals:

Increasing

: 0 < x < \frac{1}{2 6 e},

Decreasing

: \frac{1}{2 6 e} < x < \infty

Plug

x = \frac{1}{2 6 e}

into

- 3 x^{6} ln (2 x) : \frac{1}{128 e}

Maximum (\frac{1}{2 6 e}, \frac{1}{128 e})

What is the extreme f(x)=-3x^6ln(2x) ?
The extreme f(x)=-3x^6ln(2x) is Maximum(1/(2\sqrt[6]{e)}, 1/(128e))