2014-78.md

course	course_year	question_number	tags	title	year
Variational Principles	IB	78	IB 2014 Variational Principles	Paper 3, Section I, $\mathbf{6 C}$	2014

Let $f(x, y, z)=x z+y z$. Using Lagrange multipliers, find the location(s) and value of the maximum of $f$ on the intersection of the unit sphere $\left(x^{2}+y^{2}+z^{2}=1\right)$ and the ellipsoid given by $\frac{1}{4} x^{2}+\frac{1}{4} y^{2}+4 z^{2}=1$.