What is the extreme f(x)=2x^2ln(x)-15x^2 ?

The extreme f(x)=2x^2ln(x)-15x^2 is Minimum(e^7,-e^{14})

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extreme f(x)=2x^2ln(x)-15x^2

extreme points

f (x) = 2 x^{2} ln (x) - 15 x^{2}

Minimum (e^{7}, - e^{14})

Solution steps

f^{'} (x) = 4 x (ln (x) - 7)

Find intervals:

Decreasing

: 0 < x < e^{7},

Increasing

: e^{7} < x < \infty

Plug

x = e^{7}

into

2 x^{2} ln (x) - 15 x^{2} : - e^{14}

Minimum (e^{7}, - e^{14})

(x + 2) e^{\frac{1}{x}}

f (x) = - 3 sin^{2} (x)

f (x) = f (x) = 9 x^{8} + 8 x^{7} - 8 x - 11

f (x) = 3 x^{2} + 12 x y + 9 y^{2} + y^{3}

f (x) = 6 x^{2} + 2, 1 \leq x \leq 2

What is the extreme f(x)=2x^2ln(x)-15x^2 ?
The extreme f(x)=2x^2ln(x)-15x^2 is Minimum(e^7,-e^{14})