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受欢迎的函数 >

extreme 3/((x-1)(x^2-4))

解答

极值点

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

解答

极小值 (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24}), 极大值 (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

求解步骤

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

Find intervals:

递减

: - \infty < x < - 2,

递减

: - 2 < x < \frac{1 - 13}{3},

递增

: \frac{1 - 13}{3} < x < 1,

递增

: 1 < x < \frac{1 + 13}{3},

递减

: \frac{1 + 13}{3} < x < 2,

递减

: 2 < x < \infty

将

x = \frac{1 - 13}{3}

代入

\frac{3}{( x - 1 ) ( x ^{2} - 4 )} : - \frac{35 - 13 13}{24}

极小值 (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24})

将

x = \frac{1 + 13}{3}

代入

\frac{3}{( x - 1 ) ( x ^{2} - 4 )} : - \frac{35 + 13 13}{24}

极大值 (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

极小值 (\frac{1 - 13}{3}, - \frac{35 - 13 13}{24}), 极大值 (\frac{1 + 13}{3}, - \frac{35 + 13 13}{24})

作图

流行的例子

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