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受欢迎的函数 >

extreme f(x)=(4x)/(x^2+1),-3<= x<= 3

解答

极值点

f (x) = \frac{4 x}{x ^{2} + 1}, - 3 \leq x \leq 3

解答

极大值 (- 3, - \frac{6}{5}), 极小值 (- 1, - 2), 极大值 (1, 2), 极小值 (3, \frac{6}{5})

求解步骤

找到临界点:

x = - 3, x = - 1, x = 1, x = 3

\frac{4 x}{x ^{2} + 1}, - 3 \leq x \leq 3

的定义域

: - 3 \leq x \leq 3

Find intervals:

递减

: - 3 < x < - 1,

递增

: - 1 < x < 1,

递减

: 1 < x < 3

将极值点

x = - 3

代入

\frac{4 x}{x ^{2} + 1} \Rightarrow y = - \frac{6}{5}

极大值 (- 3, - \frac{6}{5})

将极值点

x = - 1

代入

\frac{4 x}{x ^{2} + 1} \Rightarrow y = - 2

极小值 (- 1, - 2)

将极值点

x = 1

代入

\frac{4 x}{x ^{2} + 1} \Rightarrow y = 2

极大值 (1, 2)

将极值点

x = 3

代入

\frac{4 x}{x ^{2} + 1} \Rightarrow y = \frac{6}{5}

极小值 (3, \frac{6}{5})

极大值 (- 3, - \frac{6}{5}), 极小值 (- 1, - 2), 极大值 (1, 2), 极小值 (3, \frac{6}{5})

作图

流行的例子

extreme f(x)=(4x)/(x^2+1),-3<= x<= 0

e x t re m e f (x) = \frac{4 x}{x ^{2} + 1}, - 3 \leq x \leq 0

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