Answer the following questions about average and instantaneous rates of change.
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
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)=sinx on the interval [0,π/3]. Compute the average rate of change of g on this interval.
(d) Part 4: (iv) Find g′(x) and evaluate it at x=π/6. Compare this value with your answer in part (iii) and explain what the comparison indicates about the graph of y=sinx on the given interval.