x^2+y^2+z^2-2x+2y-4z-10=0 确定函数z=f(x,y)的极值?
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x^2+y^2+z^2-2x+2y-4z-10=0 确定函数z=f(x,y)的极值?
x^2+y^2+z^2-2x+2y-4z-10=0 确定函数z=f(x,y)的极值?
x^2+y^2+z^2-2x+2y-4z-10=0 确定函数z=f(x,y)的极值?
x^2+y^2+z^2-2x+2y-4z-10=0 函数z=f(x,y)
可得方程如下;
(x-1)^2+(y-1)^2+(z-2)^2=16
(z-2)^2=16-(x-1)^2-(y-1)^2
(z-2)^2的最大值是16 最小值是0
所以z得最大值是6最小值是-4
极值为0和4
这个方程是一个球,因此,Z的极值就是平行于XOY平面的最高点,极值为0和4
二维函数的极值就是与平行于X轴的的直线相切的点的函数值,三位函数的极值就是与平面相切点的函数值。
方程化为
(x-1)^2+(y-1)^2+(z-2)^2=16
(z-2)^2=16-(x-1)^2-(y-1)^2
(z-2)^2的最大值是16 最小值是0
所以z得最大值是6最小值是-4
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