Science:Math Exam Resources/Courses/MATH105/April 2018/Question 03/Statement

Use the method of Lagrange multipliers to find the absolute extrema of the function $f(x,y)=(x-1)^{2}-y$ over the boundary of the ellipse ${\frac {1}{3}}y^{2}+2(x-1)^{2}=11$.

Give the maximum and minimum values ($z$ values), as well as all locations where they occur ($x$ and $y$ values). This question evaluates your proficiency with the method of Lagrange multipliers, so a solution not using this method will receive no credit.