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

The extreme f(x)=-2x+3ln(2x) is Maximum(3/2 ,-3+3ln(3))

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extreme f(x)=-2x+3ln(2x)

extreme

Maximum (\frac{3}{2}, - 3 + 3 ln (3))

Solution steps

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

Find intervals:

Increasing

: 0 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < \infty

Plug

x = \frac{3}{2}

into

- 2 x + 3 ln (2 x) : - 3 + 3 ln (3)

Maximum (\frac{3}{2}, - 3 + 3 ln (3))

What is the extreme f(x)=-2x+3ln(2x) ?
The extreme f(x)=-2x+3ln(2x) is Maximum(3/2 ,-3+3ln(3))