What is the extreme f(x)=-3x+5ln(2x),(1,3) ?

The extreme f(x)=-3x+5ln(2x),(1,3) is Maximum(5/3 ,-5+5ln(10/3))

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extreme f(x)=-3x+5ln(2x),(1,3)

extreme points

f (x) = - 3 x + 5 ln (2 x), (1, 3)

Maximum (\frac{5}{3}, - 5 + 5 ln (\frac{10}{3}))

Solution steps

Find the critical points:

x = \frac{5}{3}

Domain of

- 3 x + 5 ln (2 x), (1, 3) : 1 < x < 3

Find intervals:

Increasing

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

Decreasing

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

Plug the extreme point

x = \frac{5}{3}

into

- 3 x + 5 ln (2 x) \Rightarrow y = - 5 + 5 ln (\frac{10}{3})

Maximum (\frac{5}{3}, - 5 + 5 ln (\frac{10}{3}))

x^{2} - y^{2} + 4 x + 5 y - 4 x y

- \frac{x}{( x - 1 ) ( x - 3 ) ^{2}}

x^{2} - 4 x [- 1.4]

f (x) = - x^{4} + 2 x^{2} y - \frac{1}{2} y^{2} - 4 y + 12

f (x y) = y^{2} ln (x^{2} y)

What is the extreme f(x)=-3x+5ln(2x),(1,3) ?
The extreme f(x)=-3x+5ln(2x),(1,3) is Maximum(5/3 ,-5+5ln(10/3))