# Interpreting the Derivative

Now that we know what the derivative is and how to calculate it, let's take a look at how we can interpret it in contexts.

## Example 1

Let *P*(*t*) be the average monthly Social Security benefit for men, measured in dollars, where *t* is measured in years since 1940.

Interpret the meaning of *P*(60) = 959.79.

In the year 2000, the average Social Security benefit for men was $959.79.

Interpret the meaning of *P*'(60) = 36.33.

In the year 2000, the average Social Security benefit for men was increasing by $36.33 per year.

## Example 2

The temperature in degrees Fahrenheit of a cup of coffee placed on a desk is given by *f*(*t*) where *t* is the minutes since the coffee was poured into the cup. Interpret the following. Give units for each.

*1*. 5 minutes after the coffee was placed on the desk the temperature of the coffee is 90 degrees farenheit.

*2*. The temperature of the coffee will be 85 degrees farenheit 7 minutes after it was placed on the desk.

*3*. 5 minutes after the coffee was placed on the desk the temperature was decreasing by 3 degrees farenheit per minute.

After finishing this lesson, complete the form below: