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受欢迎的函数 >

extreme f(x)=x(10-2x)(12-2x)

解答

极值点

f (x) = x (10 - 2 x) (12 - 2 x)

解答

极大值 (\frac{11 - 31}{3}, \frac{1232 + 248 31}{27}), 极小值 (\frac{11 + 31}{3}, \frac{1232 - 248 31}{27})

求解步骤

f^{'} (x) = 4 (3 x^{2} - 22 x + 30)

Find intervals:

递增

: - \infty < x < \frac{- 31 + 11}{3},

递减

: \frac{- 31 + 11}{3} < x < \frac{31 + 11}{3},

递增

: \frac{31 + 11}{3} < x < \infty

将

x = \frac{11 - 31}{3}

代入

x (10 - 2 x) (12 - 2 x) : \frac{1232 + 248 31}{27}

极大值 (\frac{11 - 31}{3}, \frac{1232 + 248 31}{27})

将

x = \frac{11 + 31}{3}

代入

x (10 - 2 x) (12 - 2 x) : \frac{1232 - 248 31}{27}

极小值 (\frac{11 + 31}{3}, \frac{1232 - 248 31}{27})

极大值 (\frac{11 - 31}{3}, \frac{1232 + 248 31}{27}), 极小值 (\frac{11 + 31}{3}, \frac{1232 - 248 31}{27})

作图

流行的例子

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