1. The problem statement, all variables and given/known data This section describes using Rolle's theorem to find equation of envelopes by eliminating the independent variable, in this case a1. 3. The attempt at a solution By Rolle's theorem for some 0<k<1, ∂f(x,y,a+kh)/∂a = [ f(x,y,a) - f(x,y,a+h) ]/h = 0 As h→0, P→P1 ∴lim(h→0) ∂f(x,y,a+kh)/∂a = ∂f(x,y,a)/∂a I understand why ∂f(x,y,a+kh)/∂a = 0, but why must ∂f(x,y,a)/∂a = 0 too? Just because ∂f(x,y,a+kh)/∂a = 0, as you let h→0 it doesnt mean that the derivative approaches 0 as well..