1. The problem statement, all variables and given/known data Show that y can be written as a function of x near the point (x,y)=(0,0) with x3+y3=6x+2y and what y'(x) is equal to. 2. Relevant equations Implicit Function Theorem 3. The attempt at a solution By the Implicit Function Theorem, if the partial derivative of y, Fy, does NOT equal 0 at a certain point then y can be written as a function of x at that certain point. First, I set the equation to x3+y3-6x-2y=0=F(x,y) Then I use the formula: y'(x)=(-Fx)/(Fy) Thus y'(x)=(-3x2+6)/(3y2-2) In other words, I am trying to show that the partial derivatives with respect to y (Fy) does NOT equal zero. At (0,0), Fy=3(0)2-2= -2 And at y'(0,0)=-3 I am not sure if I applied the Implicit Function Theorem correctly in this problem. Can anyone see if I miss anything? Remember I ONLY have to show that that y can be written as a function of x near the point (x,y)=(0,0), nothing less or more.