I've gotten an answer for the first half of this, but not the second one, which I believe is some sort of trick question.
Find the maximum and minimum values of on the curve
by the method of Lagrange Multipliers.
I already have this half answered, and got the following:
Now for the second half, which I believe is some sort of trick question.
If is substituted into , we get a function , which has only a maximum value on . Explain how the extreme values obtained in the first part can be obtained from .
See, the issue is that is a parabola, which has a maximum at 5, but no minimum (or at least no absolute minimum). So how would you use to find the minimum values? That's what I feel is the "trick" part of the question.
If anyone could clarify the second half of the question, I'd appreciate it.