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受欢迎的函数 >

extreme-8x^{5/3}+\sqrt[3]{x}

解答

极值点

- 8 x^{\frac{5}{3}} + 3 x

解答

极小值 (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), 极大值 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

求解步骤

f^{'} (x) = - \frac{40 x ^{\frac{2}{3}}}{3} + \frac{1}{3 x ^{\frac{2}{3}}}

Find intervals:

递减

: - \infty < x < - \frac{1}{4 0 ^{\frac{3}{4}}},

递增

: - \frac{1}{4 0 ^{\frac{3}{4}}} < x < 0,

递增

: 0 < x < \frac{1}{4 0 ^{\frac{3}{4}}},

递减

: \frac{1}{4 0 ^{\frac{3}{4}}} < x < \infty

将

x = - \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

代入

- 8 x^{\frac{5}{3}} + 3 x : - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}

极小值 (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}})

将

x = \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

代入

- 8 x^{\frac{5}{3}} + 3 x : - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

极大值 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

极小值 (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), 极大值 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

作图

流行的例子

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

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

extreme f(x,y)=16x\sqrt[3]{y}-2x^2-4x-16y+2

e x t re m e f (x, y) = 16 x 3 y - 2 x^{2} - 4 x - 16 y + 2

extreme f(x)=12x^4-4x^2+6

e x t re m e f (x) = 12 x^{4} - 4 x^{2} + 6

extreme f(x)=16sin(2x),-2pi<= x<= 2pi

e x t re m e f (x) = 16 sin (2 x), - 2 π \leq x \leq 2 π

extreme (2ln(x+4))/(x+4)

e x t re m e \frac{2 ln ( x + 4 )}{x + 4}