Question: Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x,y)= y^2 - x^2 and (1/4)x^2 + y^2 = 9
I've tried solving it like I would all other questions of this type, but I get λ=4 which doesn't seem right. Am I doing something wrong or is it a DNE situation?
Hint: Use $$y^2=9-\frac{1}{4}x^2$$ and you will get a Problem in only one variable:$$f(x,\pm\sqrt{9-\frac{1}{4}x^2})=9-\frac{1}{4}x^2-x^2$$