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受欢迎的函数 >

extreme f(x)=(x^2+2)/(x+1)

解答

极值点

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

解答

极大值 (- 1 - 3, - \frac{6 + 2 3}{3}), 极小值 (- 1 + 3, \frac{6 - 2 3}{3})

求解步骤

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

Find intervals:

递增

: - \infty < x < - 1 - 3,

递减

: - 1 - 3 < x < - 1,

递减

: - 1 < x < - 1 + 3,

递增

: - 1 + 3 < x < \infty

将

x = - 1 - 3

代入

\frac{x ^{2} + 2}{x + 1} : - \frac{6 + 2 3}{3}

极大值 (- 1 - 3, - \frac{6 + 2 3}{3})

将

x = - 1 + 3

代入

\frac{x ^{2} + 2}{x + 1} : \frac{6 - 2 3}{3}

极小值 (- 1 + 3, \frac{6 - 2 3}{3})

极大值 (- 1 - 3, - \frac{6 + 2 3}{3}), 极小值 (- 1 + 3, \frac{6 - 2 3}{3})

作图

流行的例子

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