Question

What is the difference between the average rate of change of a function on the interval [x, x + h] and the derivative of the function at x?

 

 

Answer 1

The average rate of change (AROC) between two points {x, f(x)} and {x + h, f(x + h)} is given by:

AROC = f(x + h) – f(x)/h

 

For any function f(x), its derivative f\'(x) is given by the formula:

f\'(x) = limh→0{f(x + h) – f(x)}/h

 

From the above formula it is clear that the derivative of a function is the rate of change of a function when the value of h approaches 0.

From the above formula it is clear that the derivative of a function is the rate of change of a function when the value of h approaches 0.