Unformatted text preview: (Section 1.10: Difference Quotients) 1.10.3
The average velocity is 50 mph on 0, 2 in the three scenarios below.
It is the slope of the orange secant line.
We will define instantaneous velocity (or simply velocity) in Section 1.11.
• Here, the velocity is constant (50 mph). • Here, the velocity is increasing; the car is accelerating. • Here, the car overshoots the destination and then backtracks.
WARNING 1: The car’s velocity is negative in value when it is
backtracking; this happens when the graph falls. • In calculus, the Mean Value Theorem for Derivatives will imply that the car must be
going exactly 50 mph at some time value t in 0, 2 . The theorem applies in all three () () scenarios above, because s is continuous on 0, 2 and is differentiable on 0, 2 ,
meaning that its graph makes no sharp turns and does not exhibit “infinite steepness” on
0, 2 . Differentiability will be discussed in Section 1.11. § () ...
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