2010-64.md

course	course_year	question_number	tags	title	year
Optimization	IB	64	IB 2010 Optimization	Paper 2, Section I, E	2010

Consider the function $\phi$ defined by

$$\phi(b)=\inf \left{x^{2}+y^{4}: x+2 y=b\right}$$

Use the Lagrangian sufficiency theorem to evaluate $\phi(3)$. Compute the derivative $\phi^{\prime}(3)$.