What is the extreme f(x)=x^2+3(x)((500)/(x^2)) ?

The extreme f(x)=x^2+3(x)((500)/(x^2)) is Minimum(5\sqrt[3]{6},75*6^{2/3})

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extreme f(x)=x^2+3(x)((500)/(x^2))

extreme

Minimum (536, 75 \cdot 6^{\frac{2}{3}})

Solution steps

f^{'} (x) = 2 x - \frac{1500}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 536,

Increasing

: 536 < x < \infty

Plug

x = 536

into

x^{2} + 3 x \frac{500}{x ^{2}} : 75 \cdot 6^{\frac{2}{3}}

Minimum (536, 75 \cdot 6^{\frac{2}{3}})

What is the extreme f(x)=x^2+3(x)((500)/(x^2)) ?
The extreme f(x)=x^2+3(x)((500)/(x^2)) is Minimum(5\sqrt[3]{6},75*6^{2/3})