Use the graph to determine the following. (a) Find the numbers at which f has a

Question

Use the graph to determine the following. (a) Find the numbers at which f has a relative maximum. What are these relative maxima? (b) Find the numbers at which f has a relative minimum. What are these relative minima? (a) The number(s) at which f has a relative maximum is/are . (Type an integer or a decimal. Use a comma to separate answers as needed.) The relative maximum/maxima is/are . (Type an integer or a decimal. Use a comma to separate answers as needed.) (b) The number(s) at which f has a relative minimum is/are . (Type an integer or a decimal. Use a comma to separate answers as needed.) The relative minimum/minima is/are . (Type an integer or a decimal Use a comma to separate answers as needed.)

Explanation / Answer

WE SAY THAT A FUNCTION f(x) has a relative maximum value at x = a, if f(a) is greater than any value immediately preceding or follwing.

We call it a "relative" maximum because other values of the function may in fact be greater.

We say that a function f(x) has a relative minimum value at x = b, if f(b) is less than any value immediately preceding or follwing.

Again, other values of the function may in fact be less. With that understanding, then, we will drop the term relative.

The value of the function, the value of y, at either a maximum or a minimum is called an extreme value

Relative maximum at x= -1 ,x=1 , x=3

Relative minimum at x=0 ,x=2

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