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受欢迎的函数 >

extreme-x^3+2x^2+4x+7

解答

极值点

- x^{3} + 2 x^{2} + 4 x + 7

解答

极小值 (- \frac{2}{3}, \frac{149}{27}), 极大值 (2, 15)

求解步骤

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

Find intervals:

递减

: - \infty < x < - \frac{2}{3},

递增

: - \frac{2}{3} < x < 2,

递减

: 2 < x < \infty

将

x = - \frac{2}{3}

代入

- x^{3} + 2 x^{2} + 4 x + 7 : \frac{149}{27}

极小值 (- \frac{2}{3}, \frac{149}{27})

将

x = 2

代入

- x^{3} + 2 x^{2} + 4 x + 7 : 15

极大值 (2, 15)

极小值 (- \frac{2}{3}, \frac{149}{27}), 极大值 (2, 15)

作图

流行的例子

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