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受欢迎的函数 >

extreme (24)/r+2pir^2

解答

极值点

\frac{24}{r} + 2 π r^{2}

解答

极小值 (3 \frac{6}{π}, 4 \cdot 6^{\frac{2}{3}} 3 π + 2 π (\frac{6}{π})^{\frac{2}{3}})

求解步骤

f^{'} (r) = - \frac{24}{r ^{2}} + 4 π r

Find intervals:

递减

: - \infty < r < 0,

递减

: 0 < r < \frac{2 3 3}{3 4 3 π},

递增

: \frac{2 3 3}{3 4 3 π} < r < \infty

将

r = 3 \frac{6}{π}

代入

\frac{24}{r} + 2 π r^{2} : 4 \cdot 6^{\frac{2}{3}} 3 π + 2 π (\frac{6}{π})^{\frac{2}{3}}

极小值 (3 \frac{6}{π}, 4 \cdot 6^{\frac{2}{3}} 3 π + 2 π (\frac{6}{π})^{\frac{2}{3}})

作图

流行的例子

extreme f(x)=x^3+4x^2-3x+6

e x t re m e f (x) = x^{3} + 4 x^{2} - 3 x + 6

extreme f(x,y)=x^3+y^3+2x^2+4y^2+6

e x t re m e f (x, y) = x^{3} + y^{3} + 2 x^{2} + 4 y^{2} + 6

extreme f(x,y)=5+3x^2+3y^2+2y^3+x^3

e x t re m e f (x, y) = 5 + 3 x^{2} + 3 y^{2} + 2 y^{3} + x^{3}

extreme f(x)=4+x^3+y^3-3xy

e x t re m e f (x) = 4 + x^{3} + y^{3} - 3 x y

extreme x^{2/3}-6x^{-1/3}

e x t re m e x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}}