What is the extreme f(x)=-3x^2ln(4x) ?

The extreme f(x)=-3x^2ln(4x) is Maximum(1/(4sqrt(e)), 3/(32e))

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extreme f(x)=-3x^2ln(4x)

extreme

Maximum (\frac{1}{4 e}, \frac{3}{32 e})

Solution steps

f^{'} (x) = - 3 (2 x ln (4 x) + x)

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{1}{4 e}

into

- 3 x^{2} ln (4 x) : \frac{3}{32 e}

Maximum (\frac{1}{4 e}, \frac{3}{32 e})

What is the extreme f(x)=-3x^2ln(4x) ?
The extreme f(x)=-3x^2ln(4x) is Maximum(1/(4sqrt(e)), 3/(32e))