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受欢迎的函数 >

extreme f(x)=(-2x^2+14x-24)/(x^2+2x)

解答

极值点

f (x) = \frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x}

解答

极小值 (- \frac{2 ( 10 - 2 )}{3}, 610 + 19), 极大值 (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

求解步骤

f^{'} (x) = \frac{- 18 x ^{2} + 48 x + 48}{( x ^{2} + 2 x ) ^{2}}

Find intervals:

递减

: - \infty < x < - 2,

递减

: - 2 < x < \frac{2 ( 2 - 10 )}{3},

递增

: \frac{2 ( 2 - 10 )}{3} < x < 0,

递增

: 0 < x < \frac{2 ( 2 + 10 )}{3},

递减

: \frac{2 ( 2 + 10 )}{3} < x < \infty

将

x = - \frac{2 ( 10 - 2 )}{3}

代入

\frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x} : 610 + 19

极小值 (- \frac{2 ( 10 - 2 )}{3}, 610 + 19)

将

x = \frac{2 ( 2 + 10 )}{3}

代入

\frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x} : 19 - 610

极大值 (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

极小值 (- \frac{2 ( 10 - 2 )}{3}, 610 + 19), 极大值 (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

作图

流行的例子

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