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受欢迎的函数 >

extreme f(x)=310x^3-x^2-8x+48

解答

极值点

f (x) = 310 x^{3} - x^{2} - 8 x + 48

解答

极大值 (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48), 极小值 (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

求解步骤

f^{'} (x) = 930 x^{2} - 2 x - 8

Find intervals:

递增

: - \infty < x < \frac{- 7441 + 1}{930},

递减

: \frac{- 7441 + 1}{930} < x < \frac{7441 + 1}{930},

递增

: \frac{7441 + 1}{930} < x < \infty

将

x = \frac{1 - 7441}{930}

代入

310 x^{3} - x^{2} - 8 x + 48 : \frac{7441 7441 - 11161}{1297350} + 48

极大值 (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48)

将

x = \frac{1 + 7441}{930}

代入

310 x^{3} - x^{2} - 8 x + 48 : \frac{- 11161 - 7441 7441}{1297350} + 48

极小值 (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

极大值 (\frac{1 - 7441}{930}, \frac{7441 7441 - 11161}{1297350} + 48), 极小值 (\frac{1 + 7441}{930}, \frac{- 11161 - 7441 7441}{1297350} + 48)

作图

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