What is the extreme f(x)=5x^2ln(x/2) ?

The extreme f(x)=5x^2ln(x/2) is Minimum(2/(sqrt(e)),-(10)/e)

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extreme f(x)=5x^2ln(x/2)

extreme points

f (x) = 5 x^{2} ln (\frac{x}{2})

Minimum (\frac{2}{e}, - \frac{10}{e})

Solution steps

f^{'} (x) = 5 (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

5 x^{2} ln (\frac{x}{2}) : - \frac{10}{e}

Minimum (\frac{2}{e}, - \frac{10}{e})

f (x) = \frac{x}{49 + x ^{2}}

f (x) = 3 x + 1

f (x) = 25 - x^{2} + x + 3

f (x) = 6 sin (3 x)

\frac{x ^{3} - 4 x}{1 + x ^{2}}

What is the extreme f(x)=5x^2ln(x/2) ?
The extreme f(x)=5x^2ln(x/2) is Minimum(2/(sqrt(e)),-(10)/e)