A department store has two locations in a city. From 2012 through 20l6, the profits for each of the store's Iwo branches are modeled by the functions f ( x ) = − 0.44 x + 13.62 and g ( x ) = 0.51 x + 11.14 . In each model, x represents the number of years alter 2012, and f and g represent the profit, in millions of dollars. a . What is the slope of f ? Describe what this means. b . What is the slope of g ? Describe what this means. c . Find f + g , What is the slope of this function? What does this mean?
A department store has two locations in a city. From 2012 through 20l6, the profits for each of the store's Iwo branches are modeled by the functions f ( x ) = − 0.44 x + 13.62 and g ( x ) = 0.51 x + 11.14 . In each model, x represents the number of years alter 2012, and f and g represent the profit, in millions of dollars. a . What is the slope of f ? Describe what this means. b . What is the slope of g ? Describe what this means. c . Find f + g , What is the slope of this function? What does this mean?
Solution Summary: The author calculates the slope of f(x)=-0.44 and its mean where the store's two branches are modeled by the functions.
A department store has two locations in a city. From 2012 through 20l6, the profits for each of the store's Iwo branches are modeled by the functions
f
(
x
)
=
−
0.44
x
+
13.62
and
g
(
x
)
=
0.51
x
+
11.14
. In each model, x represents the number of years alter 2012, and f and g represent the profit, in millions of dollars.
a. What is the slope of f ? Describe what this means.
b. What is the slope of g ? Describe what this means.
c. Find
f
+
g
, What is the slope of this function? What does this mean?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 1 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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