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受欢迎的函数 >

extreme f(x)=e^{x^3-x}

解答

极值点

f (x) = e^{x^{3} - x}

解答

极大值 (- \frac{1}{3}, e^{\frac{2}{3 3}}), 极小值 (\frac{1}{3}, \frac{1}{e ^{\frac{2}{3 3}}})

求解步骤

f^{'} (x) = e^{x^{3} - x} (3 x^{2} - 1)

Find intervals:

递增

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

递减

: - \frac{1}{3} < x < \frac{1}{3},

递增

: \frac{1}{3} < x < \infty

将

x = - \frac{1}{3}

代入

e^{x^{3} - x} : e^{\frac{2}{3 3}}

极大值 (- \frac{1}{3}, e^{\frac{2}{3 3}})

将

x = \frac{1}{3}

代入

e^{x^{3} - x} : \frac{1}{e ^{\frac{2}{3 3}}}

极小值 (\frac{1}{3}, \frac{1}{e ^{\frac{2}{3 3}}})

极大值 (- \frac{1}{3}, e^{\frac{2}{3 3}}), 极小值 (\frac{1}{3}, \frac{1}{e ^{\frac{2}{3 3}}})

作图

流行的例子

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

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extreme f(x,y)=e^{x+y}

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

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