What is the extreme f(x)=2x^2-64ln(x) ?

The extreme f(x)=2x^2-64ln(x) is Minimum(4,32-128ln(2))

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extreme f(x)=2x^2-64ln(x)

extreme points

f (x) = 2 x^{2} - 64 ln (x)

Minimum (4, 32 - 128 ln (2))

Solution steps

f^{'} (x) = 4 x - \frac{64}{x}

Find intervals:

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 4

into

2 x^{2} - 64 ln (x) : 32 - 128 ln (2)

Minimum (4, 32 - 128 ln (2))

f (x) = e^{x - y} (x^{2} - 2 y^{2})

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

f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16

f (x) = 3 + 81 x - 3 x^{3}

f (x, y) = 20 x y - x^{3} - 10 y^{2}

What is the extreme f(x)=2x^2-64ln(x) ?
The extreme f(x)=2x^2-64ln(x) is Minimum(4,32-128ln(2))