Question 2: Use definition 2.1.1 to find out the average rate of change over the specified interval for the following functions:
Solution
a. s = 2t -3 from t = 2 to t = 5
The average rate of change is given by,
Let s(t) = 2t – 3, then s(t + Δt) = 2(t + Δt) – 3
Putting the values,
Simplifying,
b. y = x2 -6x +8 from x = 3 to x = 3.1
Let y = f(x) = x2 -6x +8 ⇒ f(x + Δx) = (x+Δx)2 – 6(x+Δx) + 8
Now rate of change is
Substituting the values,
Cancelling Δx,
Now put x = 3, Δx = 3.1 – 3 = 0.1, we have
c. A = πr2 from r = 2 to r = 2.1
Let f(r) = πr2 ⇒ f(r+Δr) = π(r+Δr)2. So the rate of change of A is,
Simplifying,
Now r = 2 and Δr = 2.1 – 2 = 0.1. Therefore, substituting in the above equation,
d. 
Let 
Put t = 9, Δt = 16 – 9 = 7
Pingback:Math’s 12, Exercise 2.1