For part a), pay attention to what info was given to you. What does differentiability imply?
Jameson
The rate of a runner running the 400 meter run in 50 seconds is given by a differentiable function r(t). The table below shows the rate as measured every 5 seconds.
Time (Seconds) Rate(m/sec)
0--------------------0
5--------------------5
10-------------------7
15-------------------10
20-------------------12
25-------------------13
30-------------------11
35-------------------9
40-------------------8
45-------------------7
50-------------------6
A.) Explain why r(t) is a continuous function.
B.) Given some time (t=c) on (0,50) and using correct units, explain the meaning of
lim ((r(c)-r(t))/(c-t))
t-->c
C.) Is there some time on the interval (0,50) such that r'(t)=0? Explain.
D.) Find the average acceleration on [10,40]. Label the answer in correct units.
E.) Approximate as accurately as possible the acceleration of the runner at t=30 seconds algebraically.