PX284 - F2b - aside on lagrange multipliers

PX275 - A5 - lagrange multipliers

• to find the minimum (or maximum) of a function, $f(x,y)$, subject to a constraint, $g(x,y)=c$
• the extrema occurs when the $g=c$ contour of the constraint, $g(x,y)$, tangentially touches a contour of the function, $f(x,y)$, ie. when $\overrightarrow{\mathrm{\nabla }}f\parallel \overrightarrow{\mathrm{\nabla }}g$, or, $\overrightarrow{\mathrm{\nabla }}f=\lambda \overrightarrow{\mathrm{\nabla }}g$, where $\lambda$ is a constant called the lagrange multiplier