Comments on lecture 1
1.1 Some ways to represent functions
DEF: Let A, B be 2 sets (usually subsets of R - the set of real numbers). A function
f : A B is a rule that assigns to each element x A a unique element, f (x), in B.
A is called the domain of th
Try the following exercises:
EXC 1 Suppose f (x) = ex x. Find the intervals where f is decreasing, and the
intervals where f is increasing.
Hint: f (x) > 0 if and only if x < 0, so f is increasing only on (, 0). f (x) < 0 i