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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{5}{2}

into

- 2 x + 5 ln (2 x) : - 5 + 5 ln (5)

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

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

f (x) = 2 cos^{2} (x), 0 \leq x \leq π

f (x, y) = x y + \frac{2}{x} + \frac{4}{y}

f (x, y) = - 5 x^{2} - 8 y^{2} - 2 x y + 42 x + 102 y

\frac{12}{x ^{2} + 1}

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