MATH 221 Exercises on Applications of the Derivative.

1. Find the domain, the critical points, the discontinuities, and the points of inflection of each of the following functions. Determine the intervals on which the functions are increasing, decreasing, concave up, and concave down. Find the local maximum and minimum points. Finally sketch the graph of the function.

a) b) c)

2. Give an example of a function (by graph and by formula) which has exactly two critical points, both of which are local maximum points.