What is the extreme f(x)=-3x^4ln(3x),(0,4) ?

The extreme f(x)=-3x^4ln(3x),(0,4) is Maximum(1/(3\sqrt[4]{e)}, 1/(108e))

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extreme f(x)=-3x^4ln(3x),(0,4)

extreme

Maximum (\frac{1}{3 4 e}, \frac{1}{108 e})

Solution steps

Find the critical points:

x = \frac{1}{3 4 e}

Domain of

- 3 x^{4} ln (3 x), (0, 4) : 0 < x < 4

Find intervals:

Increasing

: 0 < x < \frac{1}{3 4 e},

Decreasing

: \frac{1}{3 4 e} < x < 4

Plug the extreme point

x = \frac{1}{3 4 e}

into

- 3 x^{4} ln (3 x) \Rightarrow y = \frac{1}{108 e}

Maximum (\frac{1}{3 4 e}, \frac{1}{108 e})

What is the extreme f(x)=-3x^4ln(3x),(0,4) ?
The extreme f(x)=-3x^4ln(3x),(0,4) is Maximum(1/(3\sqrt[4]{e)}, 1/(108e))