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受欢迎的函数 >

extreme f(x)=-6x^{5/3}+\sqrt[3]{x}

解答

极值点

f (x) = - 6 x^{\frac{5}{3}} + 3 x

解答

极小值 (- \frac{1}{4 27000}, - 6 (- \frac{1}{4 27000})^{\frac{5}{3}} - (\frac{1}{4 27000})^{\frac{1}{3}}), 极大值 (\frac{1}{4 27000}, - 6 (\frac{1}{4 27000})^{\frac{5}{3}} + 3 \frac{1}{4 27000})

求解步骤

f^{'} (x) = \frac{1 - 30 x ^{\frac{4}{3}}}{3 x ^{\frac{2}{3}}}

Find intervals:

递减

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

递增

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

递增

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

递减

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

将

x = - \frac{1}{4 27000}

代入

- 6 x^{\frac{5}{3}} + 3 x : - 6 (- \frac{1}{4 27000})^{\frac{5}{3}} - (\frac{1}{4 27000})^{\frac{1}{3}}

极小值 (- \frac{1}{4 27000}, - 6 (- \frac{1}{4 27000})^{\frac{5}{3}} - (\frac{1}{4 27000})^{\frac{1}{3}})

将

x = \frac{1}{4 27000}

代入

- 6 x^{\frac{5}{3}} + 3 x : - 6 (\frac{1}{4 27000})^{\frac{5}{3}} + 3 \frac{1}{4 27000}

极大值 (\frac{1}{4 27000}, - 6 (\frac{1}{4 27000})^{\frac{5}{3}} + 3 \frac{1}{4 27000})

极小值 (- \frac{1}{4 27000}, - 6 (- \frac{1}{4 27000})^{\frac{5}{3}} - (\frac{1}{4 27000})^{\frac{1}{3}}), 极大值 (\frac{1}{4 27000}, - 6 (\frac{1}{4 27000})^{\frac{5}{3}} + 3 \frac{1}{4 27000})

作图

流行的例子

extreme y=8+2/x

e x t re m e y = 8 + \frac{2}{x}

extreme f(x)=sqrt(49-x^2),(-7,7)

e x t re m e f (x) = 49 - x^{2}, (- 7, 7)

extreme 40x^3+9x^2-12x-8

e x t re m e 40 x^{3} + 9 x^{2} - 12 x - 8

extreme f(x,y)=(x^2+3y^2)e^{1-x^2-y^2}

e x t re m e f (x, y) = (x^{2} + 3 y^{2}) e^{1 - x^{2} - y^{2}}

extreme f(y)=-x^3-5x^2-7x+3

e x t re m e f (y) = - x^{3} - 5 x^{2} - 7 x + 3