What is the extreme f(x)=7x-5xln(x) ?

The extreme f(x)=7x-5xln(x) is Maximum(e^{2/5},5e^{2/5})

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extreme f(x)=7x-5xln(x)

extreme points

f (x) = 7 x - 5 x ln (x)

Maximum (e^{\frac{2}{5}}, 5 e^{\frac{2}{5}})

Solution steps

f^{'} (x) = - 5 ln (x) + 2

Find intervals:

Increasing

: 0 < x < e^{\frac{2}{5}},

Decreasing

: e^{\frac{2}{5}} < x < \infty

Plug

x = e^{\frac{2}{5}}

into

7 x - 5 x ln (x) : 5 e^{\frac{2}{5}}

Maximum (e^{\frac{2}{5}}, 5 e^{\frac{2}{5}})

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

f (x, y) = x^{2} + y^{2} + x y^{2} - 10

f (x) = x^{4} - 2 x^{3}, - 2 \leq x \leq 2

f (x) = \frac{7 x}{x ^{2} - 49}

f (x, y) = 9 x^{3} + \frac{y ^{3}}{3} - 4 x y

What is the extreme f(x)=7x-5xln(x) ?
The extreme f(x)=7x-5xln(x) is Maximum(e^{2/5},5e^{2/5})