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受欢迎的函数 >

extreme f(x)=x^3+x^2-46x+80

解答

极值点

f (x) = x^{3} + x^{2} - 46 x + 80

解答

极大值 (- \frac{1 + 139}{3}, \frac{416 + 278 139}{27} + 80), 极小值 (\frac{- 1 + 139}{3}, \frac{416 - 278 139}{27} + 80)

求解步骤

f^{'} (x) = 3 x^{2} + 2 x - 46

Find intervals:

递增

: - \infty < x < \frac{- 139 - 1}{3},

递减

: \frac{- 139 - 1}{3} < x < \frac{139 - 1}{3},

递增

: \frac{139 - 1}{3} < x < \infty

将

x = - \frac{1 + 139}{3}

代入

x^{3} + x^{2} - 46 x + 80 : \frac{416 + 278 139}{27} + 80

极大值 (- \frac{1 + 139}{3}, \frac{416 + 278 139}{27} + 80)

将

x = \frac{- 1 + 139}{3}

代入

x^{3} + x^{2} - 46 x + 80 : \frac{416 - 278 139}{27} + 80

极小值 (\frac{- 1 + 139}{3}, \frac{416 - 278 139}{27} + 80)

极大值 (- \frac{1 + 139}{3}, \frac{416 + 278 139}{27} + 80), 极小值 (\frac{- 1 + 139}{3}, \frac{416 - 278 139}{27} + 80)

作图

流行的例子

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