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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.

Consider the following problem A bicyclist is riding on a path modeled by the function fx 0038x x2 where x and fx are measured in miles Find the rate of change class=

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Answer:

The rate of change of elevation is 0.18

Explanation:

Given the function:

[tex]f(x)=0.03(8x-x^2)[/tex]

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

[tex]f^{\prime}(x)=0.03(8-2x)[/tex]

At the point x = 1, we have:

[tex]\begin{gathered} f^{\prime}(1)=0.03(8-2) \\ =0.03(6)=0.18 \end{gathered}[/tex]

The rate of change of elevation is 0.18

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