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受欢迎的函数 >

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

解答

极值点

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

解答

极大值 (- 5.56991 \dots, 0.01823 \dots), 极大值 (0.82088 \dots, - 281.46593 \dots), 极小值 (3, 0), 极大值 (5.24902 \dots, 0.01450 \dots)

求解步骤

找到临界点:

x = - 5.56991 \dots, x \approx 0.82088 \dots, x = 3, x \approx 5.24902 \dots

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

的定义域

: x < 0 or 0 < x < 1 or x > 1

Find intervals:

递增

: - \infty < x < - 5.56991 \dots,

递减

: - 5.56991 \dots < x < 0,

递增

: 0 < x < 0.82088 \dots,

递减

: 0.82088 \dots < x < 1,

递减

: 1 < x < 3,

递增

: 3 < x < 5.24902 \dots,

递减

: 5.24902 \dots < x < \infty

将极值点

x = - 5.56991 \dots

代入

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )} \Rightarrow y = 0.01823 \dots

极大值 (- 5.56991 \dots, 0.01823 \dots)

将极值点

x = 0.82088 \dots

代入

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )} \Rightarrow y = - 281.46593 \dots

极大值 (0.82088 \dots, - 281.46593 \dots)

将极值点

x = 3

代入

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )} \Rightarrow y = 0

极小值 (3, 0)

将极值点

x = 5.24902 \dots

代入

\frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )} \Rightarrow y = 0.01450 \dots

极大值 (5.24902 \dots, 0.01450 \dots)

极大值 (- 5.56991 \dots, 0.01823 \dots), 极大值 (0.82088 \dots, - 281.46593 \dots), 极小值 (3, 0), 极大值 (5.24902 \dots, 0.01450 \dots)

作图

流行的例子

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