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受欢迎的函数 >

extreme 7x(1+12x^2)^{-2}

解答

极值点

7 x (1 + 12 x^{2})^{- 2}

解答

极小值 (- \frac{1}{6}, - \frac{21}{32}), 极大值 (\frac{1}{6}, \frac{21}{32})

求解步骤

f^{'} (x) = \frac{7 ( - 36 x ^{2} + 1 )}{( 12 x ^{2} + 1 ) ^{3}}

Find intervals:

递减

: - \infty < x < - \frac{1}{6},

递增

: - \frac{1}{6} < x < \frac{1}{6},

递减

: \frac{1}{6} < x < \infty

将

x = - \frac{1}{6}

代入

7 x (1 + 12 x^{2})^{- 2} : - \frac{21}{32}

极小值 (- \frac{1}{6}, - \frac{21}{32})

将

x = \frac{1}{6}

代入

7 x (1 + 12 x^{2})^{- 2} : \frac{21}{32}

极大值 (\frac{1}{6}, \frac{21}{32})

极小值 (- \frac{1}{6}, - \frac{21}{32}), 极大值 (\frac{1}{6}, \frac{21}{32})

作图

流行的例子

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extreme 7+12x-x^3

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