Mathematics

Problem

Answer the following questions about average and instantaneous rates of change. a. Part 1: (i) Define the average rate of change of a function

y=f(x)

on the interval

[a,b]

. b. Part 2: (ii) Write the limit expression that defines the derivative of

f

at a point

x=a

. c. Part 3: (iii) Let

g(x)=\sin x

on the interval

[0,\pi/3]

. Compute the average rate of change of

g

on this interval. d. Part 4: (iv) Find

g'(x)

and evaluate it at

x=\pi/6

. Compare this value with your answer in part (iii) and explain what the comparison indicates about the graph of

y=\sin x

on the given interval.