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受欢迎的函数 >

extreme 30x^3-19x^2-14x+8

解答

极值点

30 x^{3} - 19 x^{2} - 14 x + 8

解答

极大值 (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8), 极小值 (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

求解步骤

f^{'} (x) = 90 x^{2} - 38 x - 14

Find intervals:

递增

: - \infty < x < \frac{- 1621 + 19}{90},

递减

: \frac{- 1621 + 19}{90} < x < \frac{1621 + 19}{90},

递增

: \frac{1621 + 19}{90} < x < \infty

将

x = \frac{19 - 1621}{90}

代入

30 x^{3} - 19 x^{2} - 14 x + 8 : \frac{1621 1621 - 42769}{12150} + 8

极大值 (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8)

将

x = \frac{19 + 1621}{90}

代入

30 x^{3} - 19 x^{2} - 14 x + 8 : \frac{- 42769 - 1621 1621}{12150} + 8

极小值 (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

极大值 (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8), 极小值 (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

作图

流行的例子

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