The function gives the distance (miles) in terms of time (hours). If the average rate of change of s(t) on 0<=t<=4 is 300 mph. what is the average rate of change of 1/5 s(t) on this interval?

Answer 1

Given information:

1. Average rate of change of s(t) on [0, 4] is 300 mph
2. This means: [s(4) - s(0)]/4 = 300

Find: Average rate of change of (1/5)s(t) on [0, 4]

Let g(t) = (1/5)s(t)

Average rate of change of g(t) = [g(4) - g(0)]/(4 - 0)

= [(1/5)s(4) - (1/5)s(0)]/4

= (1/5)[s(4) - s(0)]/4

= (1/5) × [s(4) - s(0)]/4

= (1/5) × 300

= 60 mph

The average rate of change is scaled by the same factor (1/5) as the function itself.