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受欢迎的函数 >

extreme f(x)=4x^3-39x^2+90x-6

解答

极值点

f (x) = 4 x^{3} - 39 x^{2} + 90 x - 6

解答

极大值 (\frac{3}{2}, \frac{219}{4}), 极小值 (5, - 31)

求解步骤

f^{'} (x) = 12 x^{2} - 78 x + 90

Find intervals:

递增

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

递减

: \frac{3}{2} < x < 5,

递增

: 5 < x < \infty

将

x = \frac{3}{2}

代入

4 x^{3} - 39 x^{2} + 90 x - 6 : \frac{219}{4}

极大值 (\frac{3}{2}, \frac{219}{4})

将

x = 5

代入

4 x^{3} - 39 x^{2} + 90 x - 6 : - 31

极小值 (5, - 31)

极大值 (\frac{3}{2}, \frac{219}{4}), 极小值 (5, - 31)

作图

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