Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 3.2, Problem 22S
To determine
To sketch: the derivative of the function.
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2. Suppose the graph below left is the function f(x). In the space below, describe what
transformations are occuring in the transformed function 3ƒ(-2x) + 1. The graph it on the
coordinate plane below right. (4 points)
1
1. Suppose we have the function f(x) = = and then we transform it by moving it four units to the
right and six units down, reflecting it horizontally, and stretching vertically by 5 units. What will
the formula of our new function g(x) be? (2 points)
g(x) =
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
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increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
Chapter 3 Solutions
Calculus
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