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受欢迎的函数 >

extreme f(x)=x^4+6x^5-x

解答

极值点

f (x) = x^{4} + 6 x^{5} - x

解答

极大值 (- 0.46495 \dots, 0.38131 \dots), 极小值 (0.39747 \dots, - 0.31299 \dots)

求解步骤

找到临界点:

x \approx - 0.46495 \dots, x \approx 0.39747 \dots

x^{4} + 6 x^{5} - x

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < - 0.46495 \dots,

递减

: - 0.46495 \dots < x < 0.39747 \dots,

递增

: 0.39747 \dots < x < \infty

将极值点

x = - 0.46495 \dots

代入

x^{4} + 6 x^{5} - x \Rightarrow y = 0.38131 \dots

极大值 (- 0.46495 \dots, 0.38131 \dots)

将极值点

x = 0.39747 \dots

代入

x^{4} + 6 x^{5} - x \Rightarrow y = - 0.31299 \dots

极小值 (0.39747 \dots, - 0.31299 \dots)

极大值 (- 0.46495 \dots, 0.38131 \dots), 极小值 (0.39747 \dots, - 0.31299 \dots)

作图

流行的例子

extreme f(x)=-2x^2+8x-1

e x t re m e f (x) = - 2 x^{2} + 8 x - 1

extreme f(x)=x^3-12x-8

e x t re m e f (x) = x^{3} - 12 x - 8

extreme f(x)=7x-2xln(x)

e x t re m e f (x) = 7 x - 2 x ln (x)

extreme f(x)=-x^3-9x^2-24x+2

e x t re m e f (x) = - x^{3} - 9 x^{2} - 24 x + 2

extreme f(x)=sqrt(x^2+y^2+5)

e x t re m e f (x) = x^{2} + y^{2} + 5