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受欢迎的函数 >

extreme f(x)=x(25-37+2x)(37/2-x)

解答

极值点

f (x) = x (25 - 37 + 2 x) (\frac{37}{2} - x)

解答

极小值 (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), 极大值 (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

求解步骤

f^{'} (x) = - 6 x^{2} + 98 x - 222

Find intervals:

递减

: - \infty < x < \frac{- 1069 + 49}{6},

递增

: \frac{- 1069 + 49}{6} < x < \frac{1069 + 49}{6},

递减

: \frac{1069 + 49}{6} < x < \infty

将

x = \frac{49 - 1069}{6}

代入

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{19747 - 1069 1069}{54}

极小值 (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54})

将

x = \frac{49 + 1069}{6}

代入

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1069 1069 + 19747}{54}

极大值 (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

极小值 (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), 极大值 (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

作图

流行的例子

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