What is the extreme f(x)=-5x+3ln(4x),(0,4) ?

The extreme f(x)=-5x+3ln(4x),(0,4) is Maximum(3/5 ,-3+3ln(12/5))

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extreme f(x)=-5x+3ln(4x),(0,4)

extreme points

f (x) = - 5 x + 3 ln (4 x), (0, 4)

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

Solution steps

Find the critical points:

x = \frac{3}{5}

Domain of

- 5 x + 3 ln (4 x), (0, 4) : 0 < x < 4

Find intervals:

Increasing

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

Decreasing

: \frac{3}{5} < x < 4

Plug the extreme point

x = \frac{3}{5}

into

- 5 x + 3 ln (4 x) \Rightarrow y = - 3 + 3 ln (\frac{12}{5})

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

f (x) = x^{2} y - 15 x y^{2} + 12 y

f (x) = x^{3} - 9 x^{2} + 15 x + 3

f (x, y) = 2 x^{3} - y^{2} - 6 x y + 23

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

f (x) = 2 x^{3} + 3 x^{2} - 12 x - 18

What is the extreme f(x)=-5x+3ln(4x),(0,4) ?
The extreme f(x)=-5x+3ln(4x),(0,4) is Maximum(3/5 ,-3+3ln(12/5))