2020-37.md

course	course_year	question_number	tags	title	year
Variational Principles	IB	37	IB 2020 Variational Principles	Paper 2, Section I, D	2020

Find the stationary points of the function $\phi=x y z$ subject to the constraint $x+a^{2} y^{2}+z^{2}=b^{2}$, with $a, b>0$. What are the maximum and minimum values attained by $\phi$, subject to this constraint, if we further restrict to $x \geqslant 0$ ?