1. The problem statement, all variables and given/known data This section describes the "Lagrange undetermined multipliers" method to find a maxima/minima point, which i have several problems at the end. 3. The attempt at a solution Why are they adding the respective contributions d(f + λg), instead of equating df = λdg ? Imagine f(x,y) as the function in the 2nd picture attached, and g(x,y) = c as an equation of a circle. We know that the constraint is g(x,y) = c so therefore all possible points (x,y) from the origin must follow g(x,y) = c. Then somewhere in f(x,y) there is a minima point (Point B) that also lie on g(x,y). We know that: => This point B must satisfy df = (∂f/∂x)dx + (∂f/∂y)dy = 0 and must satisfy g(x,y) = c To solve for this point B, we simply equate df = λdg. Why are they adding them? It's like adding the graph of y = sin x + cos x to find the intersection between them, instead of equating sin x = cos x.