What is the extreme f(x)=-5x+2ln(2x) ?

The extreme f(x)=-5x+2ln(2x) is Maximum(2/5 ,-2+2ln(4/5))

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extreme f(x)=-5x+2ln(2x)

extreme

Maximum (\frac{2}{5}, - 2 + 2 ln (\frac{4}{5}))

Solution steps

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

Find intervals:

Increasing

: 0 < x < \frac{2}{5},

Decreasing

: \frac{2}{5} < x < \infty

Plug

x = \frac{2}{5}

into

- 5 x + 2 ln (2 x) : - 2 + 2 ln (\frac{4}{5})

Maximum (\frac{2}{5}, - 2 + 2 ln (\frac{4}{5}))

What is the extreme f(x)=-5x+2ln(2x) ?
The extreme f(x)=-5x+2ln(2x) is Maximum(2/5 ,-2+2ln(4/5))