1. The problem statement, all variables and given/known data Suppose that r = f (θ) defines a polar graph. Find an expression for dx/dθ. It should not involve the letter r. Explain a procedure to determine the farthest that the graph r = f (θ) extends to the left and to the right (Hint: If x = x0 is the x - value of the point that is farthest left, how does x0 compare with all other x-values?). 2. Relevant equations 3. The attempt at a solution The wording of the question seems a bit off especially the hint "is the x - value of the point that is farthest left". Here is how I started teh problem. I know that x=r*cos(θ) so i subsituded r for f(θ) to get x=f(θ)cos(θ). My guess is that when the derivative of dx/dθ is equal to 0 then that means that the polar graph is turning back around so I take the derivative of x to get dx/dθ =-f(θ)sin(θ) +f'(θ)cos(θ) then I set it equal to 0 to get -f(θ)sin(θ) +f'(θ)cos(θ)=0 f(θ)sin(θ) =f'(θ)cos(θ) tan(θ)=f'(θ)/f(θ) tan(θ)=f'(θ)/(x/cos(θ)) x=(f'(θ) tan(θ)cos(θ)) I don't really know what I'm doing at this point. How should I approach this problem?