Problem on Finding Minimum Value - Multivariable Calculus
I am having trouble understanding a solution to the following problem in multivariable calculus. Could someone please answer my question posted beneath the actual problem and solution below?
Thank you very much!
Problem: Find an equation of the plane that passes through the point (1, 2, 3) and cuts off the smallest volume in the first octant.
Solution:Please see below.
Question: Could someone please explain the step in red? I don't understand why the equation of the tetrahedron (which seems to be something fixed) is differentiated with respect to and , the x- and y-intercepts of the tetrahedron?
I know that doing so gives you two constraints for this minimization problem, but why else for these differentiations?