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受欢迎的函数 >

extreme f(x)=-x^4+16x^3-16x+11

解答

极值点

f (x) = - x^{4} + 16 x^{3} - 16 x + 11

解答

极大值 (- 0.56423 \dots, 17.05231 \dots), 极小值 (0.59214 \dots, 4.72476 \dots), 极大值 (11.97209 \dots, 6731.22291 \dots)

求解步骤

找到临界点:

x \approx - 0.56423 \dots, x \approx 0.59214 \dots, x = 11.97209 \dots

- x^{4} + 16 x^{3} - 16 x + 11

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < - 0.56423 \dots,

递减

: - 0.56423 \dots < x < 0.59214 \dots,

递增

: 0.59214 \dots < x < 11.97209 \dots,

递减

: 11.97209 \dots < x < \infty

将极值点

x = - 0.56423 \dots

代入

- x^{4} + 16 x^{3} - 16 x + 11 \Rightarrow y = 17.05231 \dots

极大值 (- 0.56423 \dots, 17.05231 \dots)

将极值点

x = 0.59214 \dots

代入

- x^{4} + 16 x^{3} - 16 x + 11 \Rightarrow y = 4.72476 \dots

极小值 (0.59214 \dots, 4.72476 \dots)

将极值点

x = 11.97209 \dots

代入

- x^{4} + 16 x^{3} - 16 x + 11 \Rightarrow y = 6731.22291 \dots

极大值 (11.97209 \dots, 6731.22291 \dots)

极大值 (- 0.56423 \dots, 17.05231 \dots), 极小值 (0.59214 \dots, 4.72476 \dots), 极大值 (11.97209 \dots, 6731.22291 \dots)

作图

流行的例子

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