Question

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.

Answer 1

The Path of Bicyclist is given by

f(x)=0.06 x

Replacing , f(x) by , y in th above equation

y=0.06 x

This is equation of Straight line passing through Origin.

→When, x=2

y=0.06 × 2

y=0.12

→When, x=0

y=0.06 × 0

y=0

Rate of Change of Elevation

`=(f(2)-f(0))/(2-0)\\\\=(0.12-0)/(2)\\\\=0.06`

Answer 2

The following question is sort of a trick question where you are provided with unnecessary information. The elevation of the bike is modeled using the following function:

f(x) = 0.06x

We are then asked what the rate of change of the elevation is at x = 2. However, this is a linear function, and the rate of change at ANY point is equation to the slope of the function. And the slope of the function here is 0.06, therefore we did not need the value x = 2.

Rate of change = 0.06 miles/time