Lagrange Multipliers:
Find the Max and Min of x^2+y^2 given the constraint: 9x^2+4y^2=25

Question

Lagrange Multipliers:
Find the Max and Min of x^2+y^2 given the constraint: 9x^2+4y^2=25

anonymous · Answer

I found the critical values +/- 1/3 for x and +/- 3/4 for y, but I'm not sure whether these would give me the max or min.

abb0t · Answer

Well, you know that possible solutions lies on a disk of radius 5 which is a closed and bounded region, yes.

anonymous · Answer

Not sure if my critical values are correct. Even if they are, should I just plug them back into the original function to find max and min?

abb0t · Answer

Plug it into your original fnction now that you have them.

anonymous · Answer

I tried doing that, but both coordinates gave me the same output. How would I use the constraint to find the min?

abb0t · Answer

did you take the partial?

anonymous · Answer

I took the partial of the constraint and solved for lambda:
d/dx: 1=(lambda)(18x)
d/dy: 1=(lambda)(8y)

anonymous · Answer

lambda=1/18x and 1/8y
Not sure if that's correct.