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受欢迎的函数 >

extreme f(x)=x^4-4x^3-x^2+12x-2

解答

极值点

f (x) = x^{4} - 4 x^{3} - x^{2} + 12 x - 2

解答

极小值 (- 0.93853 \dots, - 10.06054 \dots), 极大值 (1.14370 \dots, 6.14327 \dots), 极小值 (2.79483 \dots, - 2.58273 \dots)

求解步骤

找到临界点:

x \approx - 0.93853 \dots, x = 1.14370 \dots, x \approx 2.79483 \dots

x^{4} - 4 x^{3} - x^{2} + 12 x - 2

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 0.93853 \dots,

递增

: - 0.93853 \dots < x < 1.14370 \dots,

递减

: 1.14370 \dots < x < 2.79483 \dots,

递增

: 2.79483 \dots < x < \infty

将极值点

x = - 0.93853 \dots

代入

x^{4} - 4 x^{3} - x^{2} + 12 x - 2 \Rightarrow y = - 10.06054 \dots

极小值 (- 0.93853 \dots, - 10.06054 \dots)

将极值点

x = 1.14370 \dots

代入

x^{4} - 4 x^{3} - x^{2} + 12 x - 2 \Rightarrow y = 6.14327 \dots

极大值 (1.14370 \dots, 6.14327 \dots)

将极值点

x = 2.79483 \dots

代入

x^{4} - 4 x^{3} - x^{2} + 12 x - 2 \Rightarrow y = - 2.58273 \dots

极小值 (2.79483 \dots, - 2.58273 \dots)

极小值 (- 0.93853 \dots, - 10.06054 \dots), 极大值 (1.14370 \dots, 6.14327 \dots), 极小值 (2.79483 \dots, - 2.58273 \dots)

作图

流行的例子

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