What is the extreme f(x)=7x-2xln(x) ?

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

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extreme f(x)=7x-2xln(x)

extreme points

f (x) = 7 x - 2 x ln (x)

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

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

into

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

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

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