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受欢迎的函数 >

extreme f(x)=x^4-4x^3+3x+5

解答

极值点

f (x) = x^{4} - 4 x^{3} + 3 x + 5

解答

极小值 (- 0.46522 \dots, 4.05393 \dots), 极大值 (0.55370 \dots, 6.07607 \dots), 极小值 (2.91152 \dots, - 13.13000 \dots)

求解步骤

找到临界点:

x \approx - 0.46522 \dots, x \approx 0.55370 \dots, x = 2.91152 \dots

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

的定义域

: - \infty < x < \infty

Find intervals:

递减

: - \infty < x < - 0.46522 \dots,

递增

: - 0.46522 \dots < x < 0.55370 \dots,

递减

: 0.55370 \dots < x < 2.91152 \dots,

递增

: 2.91152 \dots < x < \infty

将极值点

x = - 0.46522 \dots

代入

x^{4} - 4 x^{3} + 3 x + 5 \Rightarrow y = 4.05393 \dots

极小值 (- 0.46522 \dots, 4.05393 \dots)

将极值点

x = 0.55370 \dots

代入

x^{4} - 4 x^{3} + 3 x + 5 \Rightarrow y = 6.07607 \dots

极大值 (0.55370 \dots, 6.07607 \dots)

将极值点

x = 2.91152 \dots

代入

x^{4} - 4 x^{3} + 3 x + 5 \Rightarrow y = - 13.13000 \dots

极小值 (2.91152 \dots, - 13.13000 \dots)

极小值 (- 0.46522 \dots, 4.05393 \dots), 极大值 (0.55370 \dots, 6.07607 \dots), 极小值 (2.91152 \dots, - 13.13000 \dots)

作图

流行的例子

定义域 f(x)=(8x-3)/x

d o main f (x) = \frac{8 x - 3}{x}

对称性 y-6=(x+2)^2

sy mm e t ry y - 6 = (x + 2)^{2}

距离 (0,0),(3,2)

d i s t an ce (0, 0), (3, 2)

直线 (8,0),(0,-3)

l in e (8, 0), (0, - 3)

值域 f(x)=(x-1)^3+2

r an g e f (x) = (x - 1)^{3} + 2