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受欢迎的函数 >

extreme 5x^4+x^3-9x^2+2x+5

解答

极值点

5 x^{4} + x^{3} - 9 x^{2} + 2 x + 5

解答

极小值 (- 1.07435 \dots, - 2.11558 \dots), 极大值 (0.11500 \dots, 5.11337 \dots), 极小值 (0.80934 \dots, 3.39887 \dots)

求解步骤

找到临界点:

x = - 1.07435 \dots, x \approx 0.11500 \dots, x \approx 0.80934 \dots

5 x^{4} + x^{3} - 9 x^{2} + 2 x + 5

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 1.07435 \dots,

递增

: - 1.07435 \dots < x < 0.11500 \dots,

递减

: 0.11500 \dots < x < 0.80934 \dots,

递增

: 0.80934 \dots < x < \infty

将极值点

x = - 1.07435 \dots

代入

5 x^{4} + x^{3} - 9 x^{2} + 2 x + 5 \Rightarrow y = - 2.11558 \dots

极小值 (- 1.07435 \dots, - 2.11558 \dots)

将极值点

x = 0.11500 \dots

代入

5 x^{4} + x^{3} - 9 x^{2} + 2 x + 5 \Rightarrow y = 5.11337 \dots

极大值 (0.11500 \dots, 5.11337 \dots)

将极值点

x = 0.80934 \dots

代入

5 x^{4} + x^{3} - 9 x^{2} + 2 x + 5 \Rightarrow y = 3.39887 \dots

极小值 (0.80934 \dots, 3.39887 \dots)

极小值 (- 1.07435 \dots, - 2.11558 \dots), 极大值 (0.11500 \dots, 5.11337 \dots), 极小值 (0.80934 \dots, 3.39887 \dots)

作图

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