What is the extreme f(x)=-5x+3ln(4x) ?

The extreme f(x)=-5x+3ln(4x) is Maximum(3/5 ,-3+3ln(12/5))

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extreme f(x)=-5x+3ln(4x)

extreme points

f (x) = - 5 x + 3 ln (4 x)

Maximum (\frac{3}{5}, - 3 + 3 ln (\frac{12}{5}))

Solution steps

f^{'} (x) = - 5 + \frac{3}{x}

Find intervals:

Increasing

: 0 < x < \frac{3}{5},

Decreasing

: \frac{3}{5} < x < \infty

Plug

x = \frac{3}{5}

into

- 5 x + 3 ln (4 x) : - 3 + 3 ln (\frac{12}{5})

Maximum (\frac{3}{5}, - 3 + 3 ln (\frac{12}{5}))

f (x) = \frac{3 x}{x ^{2} + 1}

f (x) = \frac{x ^{3} + 8}{x}

f (x) = x^{3} - \frac{9}{2} x^{2} + 1

y = 2 x^{2} + z^{2}

f (x, y) = 1 - 3 x^{4} - 6 x^{2} y + 2 y^{3}

What is the extreme f(x)=-5x+3ln(4x) ?
The extreme f(x)=-5x+3ln(4x) is Maximum(3/5 ,-3+3ln(12/5))