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受欢迎的函数 >

extreme f(x)=2x^4+x^3-15x^2-9x-27

解答

极值点

f (x) = 2 x^{4} + x^{3} - 15 x^{2} - 9 x - 27

解答

极小值 (- 1.98118 \dots, - 45.00935 \dots), 极大值 (- 0.29817 \dots, - 25.66075 \dots), 极小值 (1.90436 \dots, - 65.32745 \dots)

求解步骤

找到临界点:

x = - 1.98118 \dots, x \approx - 0.29817 \dots, x \approx 1.90436 \dots

2 x^{4} + x^{3} - 15 x^{2} - 9 x - 27

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 1.98118 \dots,

递增

: - 1.98118 \dots < x < - 0.29817 \dots,

递减

: - 0.29817 \dots < x < 1.90436 \dots,

递增

: 1.90436 \dots < x < \infty

将极值点

x = - 1.98118 \dots

代入

2 x^{4} + x^{3} - 15 x^{2} - 9 x - 27 \Rightarrow y = - 45.00935 \dots

极小值 (- 1.98118 \dots, - 45.00935 \dots)

将极值点

x = - 0.29817 \dots

代入

2 x^{4} + x^{3} - 15 x^{2} - 9 x - 27 \Rightarrow y = - 25.66075 \dots

极大值 (- 0.29817 \dots, - 25.66075 \dots)

将极值点

x = 1.90436 \dots

代入

2 x^{4} + x^{3} - 15 x^{2} - 9 x - 27 \Rightarrow y = - 65.32745 \dots

极小值 (1.90436 \dots, - 65.32745 \dots)

极小值 (- 1.98118 \dots, - 45.00935 \dots), 极大值 (- 0.29817 \dots, - 25.66075 \dots), 极小值 (1.90436 \dots, - 65.32745 \dots)

作图

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