KindofSlow
Junior Member
- Joined
- Mar 5, 2010
- Messages
- 90
Hello,
Problem is find abs min & abs max of f(x,y)=2(x^2)-(y^2)+6y on disk x^2+y^2<or=16
Step 1 - Finding internal critical point (0,3) and f(0,3)=9 is easy - did this part with no problem.
Then must find critical point on boundary.
x^2=16-y^2 so g(y)=-3(y^2)+6y+32
I understand the mechanics but I don't understand conceptually what g(y) is.
I thought it would be the intersection of f(x,y) and outside of the disk (looking down would be a circle and side view would follow contours of f(x,y).
But g(y) is obviously parabolic so I thought wrong.
g(y) does not equal x, g(y) does not equal z, and g(y) does not equal f(x,y)
Can you give me any insight regarding either g(y) the curve and/or g(y) for a specific y?
Hope this makes sense.
Thank you
Problem is find abs min & abs max of f(x,y)=2(x^2)-(y^2)+6y on disk x^2+y^2<or=16
Step 1 - Finding internal critical point (0,3) and f(0,3)=9 is easy - did this part with no problem.
Then must find critical point on boundary.
x^2=16-y^2 so g(y)=-3(y^2)+6y+32
I understand the mechanics but I don't understand conceptually what g(y) is.
I thought it would be the intersection of f(x,y) and outside of the disk (looking down would be a circle and side view would follow contours of f(x,y).
But g(y) is obviously parabolic so I thought wrong.
g(y) does not equal x, g(y) does not equal z, and g(y) does not equal f(x,y)
Can you give me any insight regarding either g(y) the curve and/or g(y) for a specific y?
Hope this makes sense.
Thank you