   Chapter 3.1, Problem 13E

Chapter
Section
Textbook Problem

# (a) Sketch the graph of a function on [ − 1 , 2 ] that has an absolute maximum but no absolute minimum.(b) Sketch the graph of a function on [ − 1 , 2 ] that is discontinuous but has both an absolute maximum and an absolute minimum.

To determine

Part (a):

To sketch:

The graph of a function on -1, 2  that has an absolute maximum but no absolute minimum.

Explanation

1) Concept:

Use the concept of absolute maximum and minimum and extreme value theorem to sketch the graph of a function.

2) Definition:

Let c be a number in the domain D of a function f. Then f(c) is the absolute maximum value of f on D if fc f(x) for all x in D and absolute minimum value of f on D if fcf(x) for all x in D.

Extreme value theorem:

If f is continuous on a closed interval a, b, then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a, b].

3) Given:

A function on -1, 2  that has an absolute maximum but no absolute minimum

To determine

Part (b):

To sketch:

The graph of a function on -1, 2  that is discontinuous but has both an absolute maximum and an absolute minimum.

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