Spivak, Section 3, Problems 8, 10 (b), 13 (b), 14, 22
There were complaints that we did not have any homework problems on the Implicit Function Theorem. Here is one (you can hand in the solution and I will make comments, but I won't grade this):
Prove the Inverse Function Theorem from the Implicit Function Theorem. Hint: Given a function f from the n-th power of the real line to the n-th power of the real line, consider F(x,y)=f(x)-y and apply the Implicit Function Theorem.