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.

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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.

Calculus1
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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 \[\frac{d(f)}{d(x)} = = \frac{d}{dx}(0.06x) = 0.06\]

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