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Problem on Finding Minimum Value - Multivariable Calculus

Hello everyone,

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!

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__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?