... Characterizing Functions and Introducing Rates of Change
(a) The increase in the price of a cup of coffee in Seattle from 1970 to 2000
(b) The percent increase in the price of a cup of coffee in Seattle ... negative and
sometimes positive, but always increasing).
72 CHAPTER 2 Characterizing Functions and Introducing Rates of Change
5. Use the algebraic interpretati...
... to Functions and Their Rates of Change
PRELIMINARY EDITION
Sponsoring Editor: Laurie Rosatone
Managing Editor: Karen Guardino
Project Editor: Ellen Keohane
Marketing Manager: Michael Boezi
Manufacturing ... Windfall Software
Library of Congress Cataloging-in-Publication Data
Gottlieb, Robin (Robin Joan)
Calculus: an integrated approach to functions and their...
... Guardino, Sara Anderson, Michael Boezi, Susan Laferriere,
and Barbara Atkinson. And thanks to Elka Block and Frank Purcell, for their comments and
suggestions.
Finally, I want to thank the following ... Polynomial Functions and Their Graphs 391
◆ EXPLORATORY PROBLEMS FOR CHAPTER 11: Functions and Their Graphs:
Tinkering with Polynomials and Rational Functions 404...
... important and versatile. We can attach many different
mental pictures and representations to it; our choice of representation will often depend
upon context. Upon first exposure, the notation and ... degrees at 100 0 feet.
Q: Interpret T(H +10) and T(H) +10.
A: T(H +10) is the temperature at an altitude 10 feet higher than your current altitude.
T(H) +10 is a temperature 10...
... bushels of huckleberries per hour; Lollipop can devour L bushels of
huckleberries in C hours. Express your answers to parts (a) and (b) in terms of any or
all of the constants A, X, B, L, and C.
(a) ... manufacturer decides to switch to plastic lids and bottoms to eliminate
the taping problems. Assume that custom-made plastic lids and bottoms cost 7k
cents per square i...
... (fg)(x), and
f
g
(x), and find their
domains.
39. f(x)=ax + b and g(x) = cx + d
40. f(x)=3x + 2and g(x) = 5x − 1
41. f(x)=2x + 3and g(x) =x
2
−1
42. f(x)=
3
x+1
and g(x) =
2x
x−5
43. f(x)=
√
x and ... There are many ways of decomposing functions. For instance, suppose
h(x) =
x
2
+ 1
x
2
+ 2
and we want to find f and g such that f(g(x))=h(x). Determine which of the f...
... use demand curves to express the relationship between the price of an item
and the number of items demanded by consumers. Below is a demand curve for a certain
good. q is the quantity of the ... points (π,3 )and (−π,5)
8. Passing through point (
√
3,
√
2) and parallel to 3x − 4y = 7
9. Passing through the origin and perpendicular to πx −
√
3y = 12
10. x-intercept of
√...
... =
1
x
. For what value(s) of x is the slope of the tangent line to g equal to the
average rate of change of g on the interval indicated? Illustrate your answer to parts (a)
and (b) with pictures.
(a) ... graph of
√
x − 1 related to that of
√
x?
(b) How is the graph of the derivative of
√
x − 1 related to that of the derivative of
√
x? Illustrate with a rough sk...
... Your essay should be designed to help her.
(a) Explain the relationship between average rate of change and instantaneous rate of
change, and between secant lines and tangent lines. Your classmate ... approximations and thus narrowed in on the desired quantity. Using
analytic methods and a limiting process, we allowed the second data point to get arbitrarily
close to the...
... unknown constants, a, b, and c.
5
If one of the points we know happens to be
the vertex of the parabola (and we are aware of that), then the parabola is determined
by just the vertex and one other ... opening upward; y =−x
2
is an example of a parabola opening downward.
x = y
2
is an example of a parabola opening to the right, and x =−y
2
is an example of
a parabo...