A) find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following.

(i) 4 to 5

(ii) 4 to 4.5

(iii) 4 to 4.1

(b) find the instantaneous rate of change when r = 4.

a'(4) =

a)1. 28.26

2. 26.70

3. 25.44

b) 25.13

Step-by-step explanation:

We are given the following information in the question:

Area of circle

, where r is the radius of circle.

a) Formula:

Rate of change of area of circle =

Putting the given values we get:

1. Rate of change of circle when radius changes from 4 to 5

2. Rate of change of circle when radius changes from 4 to 4.5

3. Rate of change of circle when radius changes from 4 to 4.1

b) Instantaneous rate of change

When r = 4