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受欢迎的函数 >

extreme f(x)=60x^3-120x

解答

极值点

f (x) = 60 x^{3} - 120 x

解答

极大值 (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406), 极小值 (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

求解步骤

f^{'} (x) = 180 x^{2} - 120

Find intervals:

递增

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

递减

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

递增

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

将

x = - \frac{2}{3}

代入

60 x^{3} - 120 x : - 60 (\frac{2}{3})^{\frac{3}{2}} + 406

极大值 (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406)

将

x = \frac{2}{3}

代入

60 x^{3} - 120 x : 60 (\frac{2}{3})^{\frac{3}{2}} - 406

极小值 (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

极大值 (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406), 极小值 (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

作图

流行的例子

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