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受欢迎的函数 >

extreme f(x)=2pir^2+(1500)/r

解答

极值点

f (x) = 2 π r^{2} + \frac{1500}{r}

解答

极小值 (\frac{5 3 3}{3 π}, 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π)

求解步骤

f^{'} (r) = 4 π r - \frac{1500}{r ^{2}}

Find intervals:

递减

: - \infty < r < 0,

递减

: 0 < r < \frac{5 3 3}{3 π},

递增

: \frac{5 3 3}{3 π} < r < \infty

将

r = \frac{5 3 3}{3 π}

代入

2 π r^{2} + \frac{1500}{r} : 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π

极小值 (\frac{5 3 3}{3 π}, 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π)

作图

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