I would appreciate some help with this problem, I have some ideas how to approach it but I'm confused on what to do on some parts.
Consider the curve given by y^2= 2+xy
1) show that dy/dx= y/2y-x (im pretty sure i can do this if its just the derivative)
2) find all points (x,y) on the curve where the line tangent to the curve has slope 1/2 (how do u find a tangent line with a specific slope, and how would you get the points)
3) show that there are no points (x,y) on the curve where the line tangent to the curve is horizontal (this isn't horizontal asymptote right?)
4) let x and y be functions of time t that are related by the equation y^2= 2+xy. At time t=5, the value of y is 3 and dy/dt= 6. Find the value of dx/dt at time t=5 (where exactly does t go in that equation and how do i apply it?)