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

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

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extreme f(x)=-4x+5ln(2x)

extreme points

f (x) = - 4 x + 5 ln (2 x)

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = \frac{5}{4}

into

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

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

f (x, y) = x^{3} + 4 y^{2} - 3 x + 1

f (x) = 3 + 5 x - 5 x^{2}

f (x) = x^{\frac{7}{9}}

x + cos (2 x), 0 \leq x \leq π

f (x) = \frac{x ^{2}}{x ^{2} + 192}

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