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

The extreme f(x)=3x^2ln(x/2) is Minimum(2/(sqrt(e)),-6/e)

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

extreme points

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

Minimum (\frac{2}{e}, - \frac{6}{e})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{2}{e}

into

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

Minimum (\frac{2}{e}, - \frac{6}{e})

f (x, y) = \frac{1}{2} x^{2} + 2 y^{2} - 4 x - 16 y

f (x) = \frac{x + 5}{x ^{2} - x - 30}

f (x) = - x^{2} + 9, - 4 \leq x \leq 3

f (x, y) = \frac{x ^{3} + 9}{x ^{2}}

f (x) = x^{2} + 10 x y + y^{2}

What is the extreme f(x)=3x^2ln(x/2) ?
The extreme f(x)=3x^2ln(x/2) is Minimum(2/(sqrt(e)),-6/e)