What is the extreme (30)/x+3pix^2 ?

The extreme (30)/x+3pix^2 is Minimum(\sqrt[3]{5/pi},6*5^{2/3}\sqrt[3]{pi}+3pi(5/pi)^{2/3})

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extreme (30)/x+3pix^2

extreme

Minimum (3 \frac{5}{π}, 6 \cdot 5^{\frac{2}{3}} 3 π + 3 π (\frac{5}{π})^{\frac{2}{3}})

Solution steps

f^{'} (x) = - \frac{30}{x ^{2}} + 6 π x

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3 \frac{5}{π},

Increasing

: 3 \frac{5}{π} < x < \infty

Plug

x = 3 \frac{5}{π}

into

\frac{30}{x} + 3 π x^{2} : 6 \cdot 5^{\frac{2}{3}} 3 π + 3 π (\frac{5}{π})^{\frac{2}{3}}

Minimum (3 \frac{5}{π}, 6 \cdot 5^{\frac{2}{3}} 3 π + 3 π (\frac{5}{π})^{\frac{2}{3}})

What is the extreme (30)/x+3pix^2 ?
The extreme (30)/x+3pix^2 is Minimum(\sqrt[3]{5/pi},6*5^{2/3}\sqrt[3]{pi}+3pi(5/pi)^{2/3})