Coordinate Axis Scale Each function described below models the specified data for the years 2006 through 2016, with t = 6 corresponding to 2006. Estimate a reasonable scale for the vertical axis (eg., hundreds, thousands, millions, etc.) of the graph and justify your answer. (There are many correct answers.) (a) f ( t ) represents the average salary of college professors. (b) f ( t ) represents the U.S.population. (c) f ( t ) represents the percent of the civilian workforce that is unemployed. (d) f ( t ) represents the number of games a college football team wins.
Coordinate Axis Scale Each function described below models the specified data for the years 2006 through 2016, with t = 6 corresponding to 2006. Estimate a reasonable scale for the vertical axis (eg., hundreds, thousands, millions, etc.) of the graph and justify your answer. (There are many correct answers.) (a) f ( t ) represents the average salary of college professors. (b) f ( t ) represents the U.S.population. (c) f ( t ) represents the percent of the civilian workforce that is unemployed. (d) f ( t ) represents the number of games a college football team wins.
Solution Summary: The author explains how to estimate a reasonable scale for the vertical axis of the graph, using f(t) representing the average salary of college professors.
Coordinate Axis Scale Each function described below models the specified data for the years 2006 through 2016, with
t
=
6
corresponding to 2006. Estimate a reasonable scale for the vertical axis (eg., hundreds, thousands, millions, etc.) of the graph and justify your answer. (There are many correct answers.)
(a)
f
(
t
)
represents the average salary of college professors.
(b)
f
(
t
)
represents the U.S.population.
(c)
f
(
t
)
represents the percent of the civilian workforce that is unemployed.
(d)
f
(
t
)
represents the number of games a college football team wins.
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).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.