Question: Suppose that z = F(x, y) is differentiable at (a, b), that Fy(a, b) 0, and that I is an open interval containing a. Prove

Suppose that z = F(x, y) is differentiable at (a, b), that Fy(a, b) ‰ 0, and that I is an open interval containing a. Prove that if f: †’ R is differentiable at a, f(a) = b, and F(x, f(x)) = 0 for all x ˆˆ I, then

(a) = Jr (a, b) ay (a,b

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