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受欢迎的函数 >

extreme-4x^4+5x^3-x^2

解答

极值点

- 4 x^{4} + 5 x^{3} - x^{2}

解答

极大值 (0, 0), 极小值 (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768}), 极大值 (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

求解步骤

f^{'} (x) = - 16 x^{3} + 15 x^{2} - 2 x

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < \frac{15 - 97}{32},

递增

: \frac{15 - 97}{32} < x < \frac{15 + 97}{32},

递减

: \frac{15 + 97}{32} < x < \infty

将

x = 0

代入

- 4 x^{4} + 5 x^{3} - x^{2} : 0

极大值 (0, 0)

将

x = \frac{15 - 97}{32}

代入

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{4523 - 485 97}{32768}

极小值 (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768})

将

x = \frac{15 + 97}{32}

代入

- 4 x^{4} + 5 x^{3} - x^{2} : \frac{4523 + 485 97}{32768}

极大值 (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

极大值 (0, 0), 极小值 (\frac{15 - 97}{32}, \frac{4523 - 485 97}{32768}), 极大值 (\frac{15 + 97}{32}, \frac{4523 + 485 97}{32768})

作图

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