Use Python to solve each problem.

2. Find a cubic function ax3 + bx2 + cx + d whose graph has horizontal tangent lines at the points (2, 6) and (2, 0). (HINT: What do you know about f(2) and f 0 (2) ?)

3. Given g(x) = x 2 e x : a) Find and (if necessary) simplify the first five derivatives of g. b) In a print command, state the formula for the nth derivative of g. c) Test your formula by finding the 10th derivative of g.