How do you find the instantaneous rate of change of f at x=ax=a?

1 Answer
Jim H
Mar 27, 2015

By definition, the instantaneous rate of change of ff at x=ax=a is the limit of average rates of change.

The average rate of change can be written in different ways.

Because of this, the instantaneous rate of change of ff at aa can be written as either:

lim_(xrarra)(f(x)-f(a))/(x-a)

or

lim_(hrarr0)(f(a+h)-f(a))/h

In either case, attempting to find the limit by substitution lead to the indeterminate form 0/0. So techniques need to be developed to evaluate these limits. The techniques used depend on the function f.

Related questions
See all questions in Instantaneous Rate of Change at a Point
Impact of this question
3813 views around the world
You can reuse this answer
Creative Commons License