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

The extreme f(x)=3x^2ln(x/4) is Minimum(4/(sqrt(e)),-(24)/e)

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

extreme points

f (x) = 3 x^{2} ln (\frac{x}{4})

Minimum (\frac{4}{e}, - \frac{24}{e})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{4}{e}

into

3 x^{2} ln (\frac{x}{4}) : - \frac{24}{e}

Minimum (\frac{4}{e}, - \frac{24}{e})

What is the extreme f(x)=3x^2ln(x/4) ?
The extreme f(x)=3x^2ln(x/4) is Minimum(4/(sqrt(e)),-(24)/e)