In this lesson, we are going to take a look at applications of rates of change, applications of derivatives. Before we begin with the applications, we need to revise some things. If y=f(x) describes a quantity y as a function of a quantity x, then the derivative function f'(x) describes the instantaneous rate of change of y with respect to x. So, derivatives are extremely useful in all sorts of applications where one quantity changes as the other one changes. We will just look at some very simple examples of that in this video. In the first example, we'll find the rate of change of the area of a circle with respect to the radius of the circle.
gives us the rate of change of
with respect to changes in
When we evaluate
at a specific
value, we obtain an instantaneous rate of change of
with respect to
To find the units
take the units of
over the units of
Often, looking at
the units for
will help you to figure out the real world meaning of
Applications of Rates of Change
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