Finding the Rate of Elevation on a Bicyclist's Path

RunnerDP
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Homework Statement


Hi everyone, I am new to calculus. I was recently assigned some homework and am having a difficult time with it. Please help me out. Thank you!

A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - x^2), where x and f(x) are measured in miles. Find the rate of elevation when x = 2.


Homework Equations



N/A

The Attempt at a Solution



My only attempt was utilizing an equation my teacher gave me. However, the answer I got and the one on CalcChat are substantially different.


Thank you so much.
 
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RunnerDP said:

Homework Statement


Hi everyone, I am new to calculus. I was recently assigned some homework and am having a difficult time with it. Please help me out. Thank you!

A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - x^2), where x and f(x) are measured in miles. Find the rate of elevation when x = 2.


Homework Equations



N/A

The Attempt at a Solution



My only attempt was utilizing an equation my teacher gave me. However, the answer I got and the one on CalcChat are substantially different.


Thank you so much.

Is x the horizontal distance and f(x) the altitude?

You need to show us your work. We cannot possibly comment until we see what you have done already. Maybe you are right and CalcChat is wrong, or maybe the opposite is true---who knows, since you do not include either answer?
 
In particular, what was this equation your teacher gave you? Do you know how to find the derivative of f(x)?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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