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受欢迎的函数 >

extreme f(x)=(x-5)e^{-x+5-(x-5)^2}

解答

极值点

f (x) = (x - 5) e^{- x + 5 - (x - 5)^{2}}

解答

极小值 (4, - 1), 极大值 (\frac{11}{2}, \frac{1}{2 e ^{\frac{3}{4}}})

求解步骤

f^{'} (x) = - e^{- (x - 4) (x - 5)} (x - 4) (2 x - 11)

Find intervals:

递减

: - \infty < x < 4,

递增

: 4 < x < \frac{11}{2},

递减

: \frac{11}{2} < x < \infty

将

x = 4

代入

(x - 5) e^{- x + 5 - (x - 5)^{2}} : - 1

极小值 (4, - 1)

将

x = \frac{11}{2}

代入

(x - 5) e^{- x + 5 - (x - 5)^{2}} : \frac{1}{2 e ^{\frac{3}{4}}}

极大值 (\frac{11}{2}, \frac{1}{2 e ^{\frac{3}{4}}})

极小值 (4, - 1), 极大值 (\frac{11}{2}, \frac{1}{2 e ^{\frac{3}{4}}})

作图

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