Science:Math Exam Resources/Courses/MATH105/April 2014/Question 03 (a)/Hint 1

The method of Lagrange multipliers states that the extreme values of the objective function $f(x,y)$ subject to the constraint $g(x,y)=0$ will occur at the solutions to the system: $\mathrm{\nabla }f=⟨f_x,f_y⟩=\lambda ⟨g_x,g_y⟩=\lambda \mathrm{\nabla }g$.