What is the extreme f(x)=2x^2ln(x)-19x^2 ?

The extreme f(x)=2x^2ln(x)-19x^2 is Minimum(e^9,-e^{18})

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extreme f(x)=2x^2ln(x)-19x^2

extreme

Minimum (e^{9}, - e^{18})

Solution steps

f^{'} (x) = 4 x (ln (x) - 9)

Find intervals:

Decreasing

: 0 < x < e^{9},

Increasing

: e^{9} < x < \infty

Plug

x = e^{9}

into

2 x^{2} ln (x) - 19 x^{2} : - e^{18}

Minimum (e^{9}, - e^{18})

What is the extreme f(x)=2x^2ln(x)-19x^2 ?
The extreme f(x)=2x^2ln(x)-19x^2 is Minimum(e^9,-e^{18})