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受欢迎的函数 >

extreme 3x^2e^x

解答

极值点

3 x^{2} e^{x}

解答

极大值 (- 2, \frac{12}{e ^{2}}), 极小值 (0, 0)

求解步骤

f^{'} (x) = 3 (2 x e^{x} + e^{x} x^{2})

Find intervals:

递增

: - \infty < x < - 2,

递减

: - 2 < x < 0,

递增

: 0 < x < \infty

将

x = - 2

代入

3 x^{2} e^{x} : \frac{12}{e ^{2}}

极大值 (- 2, \frac{12}{e ^{2}})

将

x = 0

代入

3 x^{2} e^{x} : 0

极小值 (0, 0)

极大值 (- 2, \frac{12}{e ^{2}}), 极小值 (0, 0)

作图

流行的例子

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