What is the extreme f(x)=-4x^6ln(3x) ?

The extreme f(x)=-4x^6ln(3x) is Maximum(1/(3\sqrt[6]{e)}, 2/(2187e))

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extreme f(x)=-4x^6ln(3x)

extreme

Maximum (\frac{1}{3 6 e}, \frac{2}{2187 e})

Solution steps

f^{'} (x) = - 4 (6 x^{5} ln (3 x) + x^{5})

Find intervals:

Increasing

: 0 < x < \frac{1}{3 6 e},

Decreasing

: \frac{1}{3 6 e} < x < \infty

Plug

x = \frac{1}{3 6 e}

into

- 4 x^{6} ln (3 x) : \frac{2}{2187 e}

Maximum (\frac{1}{3 6 e}, \frac{2}{2187 e})

What is the extreme f(x)=-4x^6ln(3x) ?
The extreme f(x)=-4x^6ln(3x) is Maximum(1/(3\sqrt[6]{e)}, 2/(2187e))