1.4 Day 1 Rates of Change, Tangent Lines, and Sensitivity
Learning Goal: Use limits to determine instantaneous rates of change, slope of tangent lines, and normal
lines.
Example 1:
Find the average rate of change of over the interval . Sketch the function over the
interval.
-
24 .
,
"¥*=¥
"
12
12
-
=
-
6 .
; , ,
Average rate of change is the slope of the secant line:
Instantaneous rate of change is the slope of the tangent line at that point.
The normal line to a curve at a point is the line perpendicular to the tangent at that point.
Learning Goal: Use limits to determine instantaneous rates of change, slope of tangent lines, and normal
lines.
Example 1:
Find the average rate of change of over the interval . Sketch the function over the
interval.
-
24 .
,
"¥*=¥
"
12
12
-
=
-
6 .
; , ,
Average rate of change is the slope of the secant line:
Instantaneous rate of change is the slope of the tangent line at that point.
The normal line to a curve at a point is the line perpendicular to the tangent at that point.
