We are first asked to find the average rate of change of R(t) over the intervals [t, t + h] with t = 5 and
h = 1,
0.1, and 0.01.
Recall that the average rate of change of R over an interval [a, a + h] is the difference quotient
R(a + h) − R(a)
h
.
Organize the calculations in a table. Use
R(t) = 50 + 40t − t2 and t = 5.
First calculate the average rate of change over [5, 5 + h] for h = 1, 0.1, 0.01.
Begin with h = 1.
R(5 + 1) − R(5)
1
=
R(6) − R(5)
1
=
50 + 40 · 6 −
Incorrect: Your answer is incorrect.
2
− (50 + 40 · 5 − 52)
1
=
