Calculus question- Implicit function theorem and neighbourhood

[masamoah23]

Use the Implicit Function Theorem to show that the equation
F(x,y)= y³+y-x²= 0
may be written in the form
y = f(x) in a neighbourhood of the point (0; 0),

Hey guys, can anyone help me on the above question?

This is the working i have done thus far:

F_x=-2x and F_y=3y²+1

But i am not really sure where to go from here, any help would be greatly appreciated! Thanks

 

[Deleted member 4993]

Use the Implicit Function Theorem to show that the equation
F(x,y)= y³+y-x²= 0
may be written in the form
y = f(x) in a neighbourhood of the point (0; 0),

Hey guys, can anyone help me on the above question?

This is the working i have done thus far:

F_x=-2x and F_y=3y²+1

But i am not really sure where to go from here, any help would be greatly appreciated! Thanks

Can you state the implicit function theorem?

More importantly,

What condition the Jacobian of the function needs to satisfy - according to this theorem?

 

[masamoah23]

hi thanks but i gt it sorted. just logically manged to sort it out, thanks again!