容易的微分解题x+y=6那(x^2)y的极大值?另一题x+y=10x^2+y^2的极小值?
1个回答

1.y=6-x

带入,(x^2)y=x^2(6-x)=6x^2-x^3

d/dx=-3x^2+12x=-3x(x-4)

d2/dx2=-6x+12

当d/dx=0时,x为最小值或最大值,

x=0,4

x=0,d2/dx2=12,x=4,d2/dx2=-12

x=4为最大值,(x^2)y=(4)^2(6-4)=16x2=32

2.y=10-x

x^2+y^2=x^2+(10-x)^2=x^2+100-20x+x^2=2x^2-20x+100

d/dx=4x-20

d/dx=0,x=5

x=5,x^2+y^2=50