Function Theorem. Let G(x,y) have continuous first partial

QUESTION:

Function Theorem. Let G(x,y) have continuous first partial derivatives in the rectangle containing the point (x o ,y o ). If G(xo,y0) and the partial derivative Gy(x0,y0) then there exists a differentiable function ,defined in some interval that satisfies for all The implicit function theorem gives conditions under which the relationship G(x,y) = 0 defines y implicitly as a function of x. Use the implicitfunction theorem to show that the relationship x + y + exy, given in Example 4, defines y implicitly as a function of x near the point (0,-1).