What is the extreme f(x)=-3x+4ln(2x) ?

The extreme f(x)=-3x+4ln(2x) is Maximum(4/3 ,-4+4ln(8/3))

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extreme f(x)=-3x+4ln(2x)

extreme points

f (x) = - 3 x + 4 ln (2 x)

Maximum (\frac{4}{3}, - 4 + 4 ln (\frac{8}{3}))

Solution steps

f^{'} (x) = - 3 + \frac{4}{x}

Find intervals:

Increasing

: 0 < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < \infty

Plug

x = \frac{4}{3}

into

- 3 x + 4 ln (2 x) : - 4 + 4 ln (\frac{8}{3})

Maximum (\frac{4}{3}, - 4 + 4 ln (\frac{8}{3}))

f (x, y) = x e^{y} - x^{2} - e^{y}

f (x) = \frac{4 x + 6}{x + 2}

f (x) = (3000 x - 2 x^{2})

f (x) = 4 x^{\frac{1}{2}} - x, 0 \leq x \leq 16

- \frac{1}{2} e^{- 2 x} x - \frac{11}{4} e^{- 2 x} + C

What is the extreme f(x)=-3x+4ln(2x) ?
The extreme f(x)=-3x+4ln(2x) is Maximum(4/3 ,-4+4ln(8/3))