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受欢迎的函数 >

extreme 2(x-1)(x^2+1)(3x^2-2x+1)

解答

极值点

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1)

解答

极大值 (0.46612 \dots, - 0.93525 \dots), 极小值 (0.65382 \dots, - 0.96342 \dots)

求解步骤

找到临界点:

x \approx 0.46612 \dots, x \approx 0.65382 \dots

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1)

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < 0.46612 \dots,

递减

: 0.46612 \dots < x < 0.65382 \dots,

递增

: 0.65382 \dots < x < \infty

将极值点

x = 0.46612 \dots

代入

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1) \Rightarrow y = - 0.93525 \dots

极大值 (0.46612 \dots, - 0.93525 \dots)

将极值点

x = 0.65382 \dots

代入

2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1) \Rightarrow y = - 0.96342 \dots

极小值 (0.65382 \dots, - 0.96342 \dots)

极大值 (0.46612 \dots, - 0.93525 \dots), 极小值 (0.65382 \dots, - 0.96342 \dots)

作图

流行的例子

extreme x^3+30x+128

e x t re m e x^{3} + 30 x + 128

extreme f(x)=(x-5)e^x

e x t re m e f (x) = (x - 5) e^{x}

extreme f(x,y)=x^3-24x+y^3-10y

e x t re m e f (x, y) = x^{3} - 24 x + y^{3} - 10 y

extreme f(x)=(2x)/(x^2-2x-3)

e x t re m e f (x) = \frac{2 x}{x ^{2} - 2 x - 3}

extreme y=x^2+(250)/x

e x t re m e y = x^{2} + \frac{250}{x}