What is the extreme f(x)=5x-4ln(4x) ?

The extreme f(x)=5x-4ln(4x) is Minimum(4/5 ,4-4ln(16/5))

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extreme f(x)=5x-4ln(4x)

extreme

Minimum (\frac{4}{5}, 4 - 4 ln (\frac{16}{5}))

Solution steps

f^{'} (x) = 5 - \frac{4}{x}

Find intervals:

Decreasing

: 0 < x < \frac{4}{5},

Increasing

: \frac{4}{5} < x < \infty

Plug

x = \frac{4}{5}

into

5 x - 4 ln (4 x) : 4 - 4 ln (\frac{16}{5})

Minimum (\frac{4}{5}, 4 - 4 ln (\frac{16}{5}))

What is the extreme f(x)=5x-4ln(4x) ?
The extreme f(x)=5x-4ln(4x) is Minimum(4/5 ,4-4ln(16/5))