MATH 221 In Class Exercise on Implicit Differentiation

Names_____________________________________________________

1. Let .

a) Find using implicit differentiation.

b) For what points (x,y) does .

c) For what points (x,y) is undefined?

d) Solving the original equation for y yields . Graph the given curve by graphing the two functions on the same graph.

e) Find the equations of the tangent lines at the points found in part b). Then graph one of these lines to see that it is actually a tangent line.

f) what happens on the curve at the points found in c)?

2. Let . Repeat parts a) – f) for this curve.