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受欢迎的函数 >

extreme f(x)= 1/x ,-2<= x<= 3

解答

极值点

f (x) = \frac{1}{x}, - 2 \leq x \leq 3

解答

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

求解步骤

找到临界点:

x = - 2, x = 3

\frac{1}{x}, - 2 \leq x \leq 3

的定义域

: - 2 \leq x < 0 or 0 < x \leq 3

Find intervals:

递减

: - 2 < x < 0,

递减

: 0 < x < 3

将极值点

x = - 2

代入

\frac{1}{x} \Rightarrow y = - \frac{1}{2}

极大值 (- 2, - \frac{1}{2})

将极值点

x = 3

代入

\frac{1}{x} \Rightarrow y = \frac{1}{3}

极小值 (3, \frac{1}{3})

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

作图

流行的例子

extreme f(x)=x+3x^{2/3}

e x t re m e f (x) = x + 3 x^{\frac{2}{3}}

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extreme f(x)=(x^2)/(x^2-3)

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