1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx + dwhere a ≠0. Show that f can have zero, one, or twocritical numbers and give an example of each case.
2. Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for allxin an interval ( a , b ), then f is constant on ( a , b).
3.True or False. The product of two increasing functions isincreasing. Clarify your answer.
4. Find the point on the graph of f ( x ) = 4 − x 2 that isclosest to the point ( 0 , 1 ).
