   Chapter 3.1, Problem 22E

Chapter
Section
Textbook Problem

# Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Use the graphs and transformations of Sections 1.2 and 1.3.) f ( t ) = cos t ,    − 3 π / 2 ≤ t ≤ 3 π / 2

To determine

To sketch:

The graph of a function f by hand and then find the absolute and local maximum and minimum values of f.

Explanation

1) Concept:

Sketch the graph of f, and then use definitions of absolute and local maximum and minimum values of f.

2) Definitions:

i) 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.

ii) The number f(c) is a local maximum value of f  if fcf(x) when x is near c and local minimum value of f if fc fx  when x is near c.

3) Given:

ft=cost ; -3π2 t3π2

4) Calculation:

Sketch the graph of f(x):

From the above graph, the function has absolute maximum value f0=1 since it is the highest point on the domain of the given function. Absolute minimum value fπ= -1 & f-π=-1 since it is the lowest points on the domain of the given function

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Mathematical Applications for the Management, Life, and Social Sciences 