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受欢迎的函数 >

extreme f(x)=x^2(6-x)^3

解答

极值点

f (x) = x^{2} (6 - x)^{3}

解答

极小值 (0, 0), 极大值 (\frac{12}{5}, \frac{839808}{3125}), 鞍点 (6, 0)

求解步骤

f^{'} (x) = - x (x - 6)^{2} (5 x - 12)

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < \frac{12}{5},

递减

: \frac{12}{5} < x < 6,

递减

: 6 < x < \infty

将

x = 0

代入

x^{2} (6 - x)^{3} : 0

极小值 (0, 0)

将

x = \frac{12}{5}

代入

x^{2} (6 - x)^{3} : \frac{839808}{3125}

极大值 (\frac{12}{5}, \frac{839808}{3125})

将

x = 6

代入

x^{2} (6 - x)^{3} : 0

鞍点 (6, 0)

极小值 (0, 0), 极大值 (\frac{12}{5}, \frac{839808}{3125}), 鞍点 (6, 0)

作图

流行的例子

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