Class Drill 4: Representations of Slopes
In Section 3-4 of the textbook, you learned about average rate of change and instantaneous rate of
change.
Definition of Average Rate of Change
 words: the average rate of change of as the input changes from to
 usage: is a function that is continuous on the interval
.
 meaning: the number
 graphical interpretation: The number is the slope of the secant line that touches the graph of
at the points
and
.
 remark: The average rate of change is a number.
Definition of Instantaneous Rate of Change
 words: the instantaneous rate of change of at
 alternate words: the derivative of at
 symbol:
 meaning: the number
 graphical interpretation: The number is the slope of the line tangent to the graph of
point
.
 remark: The instantaneous rate of change
is a number.
at the
Each expression in the left column represents a number that can be interpreted as the slope of a line
on the graph of . In each example, draw the line on the graph of , or write the missing expression
based on the line shown in the graph, and then give the value of the number represented by the
expression.
Example
(1)
(2)
Expression representing
the average rate of
change of as the input
changes from to
the derivative of
at
page 14 of 48
Line whose slope is
Value of
Example
(3)
Expression representing
the instantaneous rate of
change of at
(4)
(5)
(6)
(7)
page 15 of 48
Line whose slope is
Value of