Question

1. A car travels 20 mi/hr for 2 hours and then 30 mi/hr for 3 hours.

a) For 0<t<2 let c(t) be the distance the car has traveled in miles from time 0 to time t, where t is measured in hours. Find c(t).

b) Extend your function c(t) from part (a) to the time period 2 <= t <= 5. You will have a piecewise continuous function.

c) For the function c(t) in the previous problem, find c'(1) and c'(3).

Answer 1

a) c = 20 t , 0<t<2

b) c = 40 + 30 (t-2) , 2<t<5

c) Use the first equation to get c(1) and the second equation to get c(3)

They call it c', but it's the same thing as c at the value of t selected.