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受欢迎的函数 >

extreme f(x)=(-24x^2-20x+24)/((x^2+1)^2)

解答

极值点

f (x) = \frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}}

解答

极小值 (- 2.41898 \dots, - 1.44976 \dots), 极大值 (- 0.13236 \dots, 25.33139 \dots), 极小值 (1.30134 \dots, - 5.88163 \dots)

求解步骤

找到临界点:

x = - 2.41898 \dots, x \approx - 0.13236 \dots, x \approx 1.30134 \dots

\frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}}

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 2.41898 \dots,

递增

: - 2.41898 \dots < x < - 0.13236 \dots,

递减

: - 0.13236 \dots < x < 1.30134 \dots,

递增

: 1.30134 \dots < x < \infty

将极值点

x = - 2.41898 \dots

代入

\frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}} \Rightarrow y = - 1.44976 \dots

极小值 (- 2.41898 \dots, - 1.44976 \dots)

将极值点

x = - 0.13236 \dots

代入

\frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}} \Rightarrow y = 25.33139 \dots

极大值 (- 0.13236 \dots, 25.33139 \dots)

将极值点

x = 1.30134 \dots

代入

\frac{- 24 x ^{2} - 20 x + 24}{( x ^{2} + 1 ) ^{2}} \Rightarrow y = - 5.88163 \dots

极小值 (1.30134 \dots, - 5.88163 \dots)

极小值 (- 2.41898 \dots, - 1.44976 \dots), 极大值 (- 0.13236 \dots, 25.33139 \dots), 极小值 (1.30134 \dots, - 5.88163 \dots)

作图

流行的例子

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