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Unformatted text preview: ant line through these points.
For that reason, some textbooks use the notation msec for the average rate of change of a function.
Note that for a linear function m = msec , or in other words, its rate of change over an interval is
the same as its average rate of change. 2.1 Linear Functions 121
y = f (x) (b, f (b)) (a, f (a)) The graph of y = f (x) and its secant line through (a, f (a)) and (b, f (b))
The interested reader may question the adjective ‘average’ in the phrase ‘average rate of change.’
In the ﬁgure above, we can see that the function changes wildly on [a, b], yet the slope of the secant
line only captures a snapshot of the action at a and b. This situation is entirely analogous to the
average speed on a trip. Suppose it takes you 2 hours to travel 100 miles. Your average speed is
= 50 miles per hour. However, it is entirely possible that at the start of your journey, you
traveled 25 miles per hour, then sped up to 65 miles per hour, and so forth. The average rat...
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