Your goal? Design two implicitly defined equations (cannot isolate y in terms of x) and analyze key points along the curves created by the equations. PART 1: Curve Design a) Write an implicitly defined equation using only powers of x and y. The equation must.. a. Require at least one use of product rule when differentiating b. Have at least one maximum or minimum at a point with rational coordinates (coordinates are counting numbers or can be expressed as fractions L. You can use Desmos to graph your equation and find this point. b) Find -for your equation. c) Find - for your equation in terms of x and y. d) State a point on the curve of your equation where the curve has a relative maximum or minimum. Then... a. Use the first derivative and confirm that this point is a critical point using the definition of critical point. b. Use the second derivative test for extrema to confirm this point is the correct type of relative extreme