Determine whether the statement is true or false. If it is false, give an example for which the statement fails.

a) if f has a relative maximum at x0, then f(x0) is the largest value that f(x) can have

Distinguish between relative maximum and absolute maximum.

Statement (a) is true for absolute maximum since x0 is where f(x) has the highest value over the domain of f.
Relative maximum at x0 only guarantees that f(x0)>f(x0-) and f(x0)>f(x0+), i.e. a local maximum.