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

Implicit Function Theorem. Let G(x,y) have continuous first partial derivatives in the rectangle containing the point (x _o ,y _o ). If G(x_o,y₀) and the partial derivative G_y(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 implicit

function theorem to show that the relationship x + y + e^xy, given in Example 4, defines y implicitly as a function of x near the point (0,-1).