Consider the following problem.
A bicyclist is riding on a path modeled by the function
f(x) = 0.06x,
where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at
x = 2.

Question

Consider the following problem.
A bicyclist is riding on a path modeled by the function 
f(x) = 0.06x,
 where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at 
x = 2.

jhannybean · Answer

we know the derivative is the rate of change for the function over a certain time, and because this is a linear function, the derivative is constant throughout. Therefore $$\frac{d(f)}{d(x)} = = \frac{d}{dx}(0.06x) = 0.06$$