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受欢迎的函数 >

extreme 2x^3-x^2-4x+12

解答

极值点

2 x^{3} - x^{2} - 4 x + 12

解答

极大值 (- \frac{2}{3}, \frac{368}{27}), 极小值 (1, 9)

求解步骤

f^{'} (x) = 6 x^{2} - 2 x - 4

Find intervals:

递增

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

递减

: - \frac{2}{3} < x < 1,

递增

: 1 < x < \infty

将

x = - \frac{2}{3}

代入

2 x^{3} - x^{2} - 4 x + 12 : \frac{368}{27}

极大值 (- \frac{2}{3}, \frac{368}{27})

将

x = 1

代入

2 x^{3} - x^{2} - 4 x + 12 : 9

极小值 (1, 9)

极大值 (- \frac{2}{3}, \frac{368}{27}), 极小值 (1, 9)

作图

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