What is the extreme f(x)=9x-(5x)ln(x),(0,infinity) ?

The extreme f(x)=9x-(5x)ln(x),(0,infinity) is Maximum(e^{4/5},5e^{4/5})

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extreme f(x)=9x-(5x)ln(x),(0,infinity)

extreme points

f (x) = 9 x - (5 x) ln (x), (0, \infty)

Maximum (e^{\frac{4}{5}}, 5 e^{\frac{4}{5}})

Solution steps

Find the critical points:

x = e^{\frac{4}{5}}

Domain of

9 x - 5 x ln (x), (0, \infty) : x > 0

Find intervals:

Increasing

: 0 < x < e^{\frac{4}{5}},

Decreasing

: e^{\frac{4}{5}} < x < \infty

Plug the extreme point

x = e^{\frac{4}{5}}

into

9 x - 5 x ln (x) \Rightarrow y = 5 e^{\frac{4}{5}}

Maximum (e^{\frac{4}{5}}, 5 e^{\frac{4}{5}})

f (x, y) = x^{3} + y^{3} - 27 x y

f (x) = y^{5} - 3 x y

f (x, y) = x^{2} + y^{2} - 2 x + 5 y

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

f (x, y) = - 3 x^{2} - 4 x y - 8 y^{2} + 42 x + 68 y + 4

What is the extreme f(x)=9x-(5x)ln(x),(0,infinity) ?
The extreme f(x)=9x-(5x)ln(x),(0,infinity) is Maximum(e^{4/5},5e^{4/5})