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受欢迎的函数 >

extreme x(sqrt(8-x^2))

解答

极值点

x (8 - x^{2})

解答

极大值 (- 22, 0), 极小值 (- 2, - 4), 极大值 (2, 4), 极小值 (22, 0)

求解步骤

找到临界点:

x = - 22, x = - 2, x = 2, x = 22

x 8 - x^{2}

的定义域

: - 22 \leq x \leq 22

Find intervals:

递减

: - 22 < x < - 2,

递增

: - 2 < x < 2,

递减

: 2 < x < 22

将极值点

x = - 22

代入

x 8 - x^{2} \Rightarrow y = 0

极大值 (- 22, 0)

将极值点

x = - 2

代入

x 8 - x^{2} \Rightarrow y = - 4

极小值 (- 2, - 4)

将极值点

x = 2

代入

x 8 - x^{2} \Rightarrow y = 4

极大值 (2, 4)

将极值点

x = 22

代入

x 8 - x^{2} \Rightarrow y = 0

极小值 (22, 0)

极大值 (- 22, 0), 极小值 (- 2, - 4), 极大值 (2, 4), 极小值 (22, 0)

作图

流行的例子

extreme f(x)=f(x)=-8x^2-144x+6

e x t re m e f (x) = f (x) = - 8 x^{2} - 144 x + 6

extreme f(x)=x^3-3x[0.3]

e x t re m e f (x) = x^{3} - 3 x [0.3]

extreme f(x)=(4860)/x+18x+731856

e x t re m e f (x) = \frac{4860}{x} + 18 x + 731856

extreme f(x)=3x^2+4x-6

e x t re m e f (x) = 3 x^{2} + 4 x - 6

extreme f(x,y)=(x-3)^2-(y-1)^2

e x t re m e f (x, y) = (x - 3)^{2} - (y - 1)^{2}