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受欢迎的函数 >

extreme f(x)=2x^4-7x^3+4x^2+2x+3

解答

极值点

f (x) = 2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3

解答

极小值 (- 0.16960 \dots, 2.81166 \dots), 极大值 (0.70558 \dots, 4.43935 \dots), 极小值 (2.08901 \dots, - 1.09231 \dots)

求解步骤

找到临界点:

x \approx - 0.16960 \dots, x \approx 0.70558 \dots, x = 2.08901 \dots

2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 0.16960 \dots,

递增

: - 0.16960 \dots < x < 0.70558 \dots,

递减

: 0.70558 \dots < x < 2.08901 \dots,

递增

: 2.08901 \dots < x < \infty

将极值点

x = - 0.16960 \dots

代入

2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3 \Rightarrow y = 2.81166 \dots

极小值 (- 0.16960 \dots, 2.81166 \dots)

将极值点

x = 0.70558 \dots

代入

2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3 \Rightarrow y = 4.43935 \dots

极大值 (0.70558 \dots, 4.43935 \dots)

将极值点

x = 2.08901 \dots

代入

2 x^{4} - 7 x^{3} + 4 x^{2} + 2 x + 3 \Rightarrow y = - 1.09231 \dots

极小值 (2.08901 \dots, - 1.09231 \dots)

极小值 (- 0.16960 \dots, 2.81166 \dots), 极大值 (0.70558 \dots, 4.43935 \dots), 极小值 (2.08901 \dots, - 1.09231 \dots)

作图

流行的例子

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