Exercise 16 Page 340

A point on the graph of a function is a relative maximum if no other nearby point has a greater y-coordinate. Similarly, a point is a relative minimum if no other nearby point has a lesser y-coordinate. Let's consider the graph of f(x)=x^3-2x^2-3x.

The value of f(x) at x=- 0.5 is greater than the surrounding points. Thus, there must be a relative maximum near x=- 0.5. The value of f(x) at x=1.8 is less than the surrounding points. Thus, there must be a relative minimum near x=1.8.