Question

Consider the following problem. A bicyclist is riding on a path modeled by the function f(x) = 0.03(8x − x^2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.

Answer 1

Answer:

The rate of change of elevation is 0.18

Explanation:

Given the function:

$f(x)=0.03(8x-x^2)$

To find the rate of change, we take the derivative of f(x)

$f^{\prime}(x)=0.03(8-2x)$

At the point x = 1, we have:

$\begin{gathered} f^{\prime}(1)=0.03(8-2) \\ =0.03(6)=0.18 \end{gathered}$

The rate of change of elevation is 0.18