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受欢迎的函数 >

extreme f(x)=(x^2(x-1))/(x+2),x\ne 2

解答

极值点

f (x) = \frac{x ^{2} ( x - 1 )}{x + 2}, x \neq = 2

解答

极小值 (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8}), 极大值 (0, 0), 极小值 (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

求解步骤

找到临界点:

x = \frac{- 5 - 57}{4}, x = 0, x = \frac{- 5 + 57}{4}

\frac{x ^{2} ( x - 1 )}{x + 2}, x \neq = 2

的定义域

: x < - 2 or - 2 < x < 2 or x > 2

Find intervals:

递减

: - \infty < x < \frac{- 5 - 57}{4},

递增

: \frac{- 5 - 57}{4} < x < - 2,

递增

: - 2 < x < 0,

递减

: 0 < x < \frac{- 5 + 57}{4},

递增

: \frac{- 5 + 57}{4} < x < 2,

递增

: 2 < x < \infty

将极值点

x = \frac{- 5 - 57}{4}

代入

\frac{x ^{2} ( x - 1 )}{x + 2} \Rightarrow y = \frac{19 57 + 143}{8}

极小值 (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8})

将极值点

x = 0

代入

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

极大值 (0, 0)

将极值点

x = \frac{- 5 + 57}{4}

代入

\frac{x ^{2} ( x - 1 )}{x + 2} \Rightarrow y = - \frac{19 57 - 143}{8}

极小值 (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

极小值 (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8}), 极大值 (0, 0), 极小值 (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

作图

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