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

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

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

extreme points

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

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

Solution steps

Find the critical points:

x = \frac{5}{2}

Domain of

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

Find intervals:

Increasing

: 1 < x < \frac{5}{2},

Decreasing

: \frac{5}{2} < x < 5

Plug the extreme point

x = \frac{5}{2}

into

- 2 x + 5 ln (2 x) \Rightarrow y = - 5 + 5 ln (5)

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

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3 - 2 x

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

2 cos (2 x)

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