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

1 Answer
Jim H
Mar 27, 2015

By definition, the instantaneous rate of change of #f# at #x=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 #f# at #a# 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#.

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