Consider the following problem. A bicyclist is riding on a path modeled by the f
ID: 2855918 • Letter: C
Question
Consider the following problem.
A bicyclist is riding on a path modeled by the function
f(x) = 0.09x,
where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at
x = 5.
Decide whether the problem can be solved using precalculus, or whether calculus is required.
The problem can be solved using precalculus. The problem requires calculus to be solved.
If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
2
Explanation / Answer
This problem can be solved using pre-calculus as the given function is linear.
In a linear function, y = mx + c (equation of straight line), m is the rate of change at any point on the graph. m can be found as follows:
m = (y2-y1)/(x2-x1)
where (x1,y1) and (x2,y2) are points on the graph.
In this question, we have y = f(x) = 0.09x
So, m can be found using points (0,0) and (5,0.45) on the graph:
m = (0.45-0)/(5-0) = 0.45/5 = 0.09
Hence, rate of change of the elevation is 0.09 at x = 5