1. Let f (x) = 1/x (a) Use the limit definition of derivative to find f (x). (b) Verify your answer to (a) using the Power Rule. (c) Use the Power Rule to find f (x), f (x) and f (4)(x). Find a pattern in the derivatives and make a conjecture for a formula for f (n)(x), the nth derivative of f (x).

2. Determine whether each of the following statements are true or false. If true, provide justification (calculations that justify your assertion and 1-2 sentences explaining your answer). If false, provide a counterexample (an example of a function that satisfies the hypotheses of the statement but not the conclusion, and 1-2 sentences explaining your answer).

(a) d/dx (f (x)g(x)) = f (x)g(x)

(b) Every quadratic function (i.e. every function of the form f (x) = ax2 + bx + c with a, b and c constants and a 6= 0) has exactly one tangent line that is horizontal.

(c) Every cubic function (i.e. function of the form f (x) = ax3+bx2+cx+d with a, b, c and d constants, and a 6= 0) has at least one tangent line that is horizontal.