Implicit and Explicit Differentiation The equation describes an ellipse. a. Use imp...

Implicit and Explicit Differentiation The equation describes an ellipse.

a. Use implicit differentiation to find its slope at the points (8, 3) and (8, -3).

b. Solve the equation for y, obtaining two functions, and differentiate both to find the slopes at x = 8. [Answers should agree with part (a).]

c. Use a graphing calculator to graph the two functions found in part (b) on an appropriate window. Then use NDERIV to find the derivatives at x = 8. [Your answers should agree with parts (a) and (b).]

Notice that differentiating implicitly was easier than solving for y and then differentiating.