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受欢迎的函数 >

extreme f(x)=30x^4-13x^3-54x^2-1

解答

极值点

f (x) = 30 x^{4} - 13 x^{3} - 54 x^{2} - 1

解答

极小值 (- \frac{4}{5}, - \frac{2077}{125}), 极大值 (0, - 1), 极小值 (\frac{9}{8}, - \frac{81509}{2048})

求解步骤

f^{'} (x) = 120 x^{3} - 39 x^{2} - 108 x

Find intervals:

递减

: - \infty < x < - \frac{4}{5},

递增

: - \frac{4}{5} < x < 0,

递减

: 0 < x < \frac{9}{8},

递增

: \frac{9}{8} < x < \infty

将

x = - \frac{4}{5}

代入

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - \frac{2077}{125}

极小值 (- \frac{4}{5}, - \frac{2077}{125})

将

x = 0

代入

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - 1

极大值 (0, - 1)

将

x = \frac{9}{8}

代入

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - \frac{81509}{2048}

极小值 (\frac{9}{8}, - \frac{81509}{2048})

极小值 (- \frac{4}{5}, - \frac{2077}{125}), 极大值 (0, - 1), 极小值 (\frac{9}{8}, - \frac{81509}{2048})

作图

流行的例子

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