Word Problem ! Beginning Calculus

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  • #1
I'm
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1. Homework Statement [/b]
A cyclist is riding on a path modeled by f(x)= 0.08x where f and f(x) are measured in miles. Find the rate of change in elevation when x = 2



Homework Equations



(f(∆x + x ) - f(x))/∆x
∆x[tex]\stackrel{lim}{\rightarrow}[/tex] 0



The Attempt at a Solution



I plugged everything into the formula and got

.00008 / .0001 = .08.

Is this the correct answer?
I think I'm doing something wrong here.
 

Answers and Replies

  • #2
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So you got
[tex]\lim_{\triangle x \rightarrow 0}\frac{f(\triangle x+x)+f(x)}{\triangle x}[/tex]

[tex]\lim_{\triangle x \rightarrow 0}\frac{0.08(\triangle x+x) - 0.08x}{\triangle x}[/tex]

So yes, 0.08 is the final answer.
 
  • #3
CompuChip
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Your answer looks correct, but it appears you didn't take the limit. Instead, you just plugged in an arbitrary value for [itex]\Delta x[/itex]. Just leave it as it is: what is [itex]f(x + \Delta x) - f(x)[/itex] when you plug in the definition of f?
 
  • #4
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1. Homework Statement [/b]
A cyclist is riding on a path modeled by f(x)= 0.08x where f and f(x) are measured in miles.
Make that "where x and f(x) are measured in miles."
Find the rate of change in elevation when x = 2



Homework Equations



(f(∆x + x ) - f(x))/∆x
∆x[tex]\stackrel{lim}{\rightarrow}[/tex] 0



The Attempt at a Solution



I plugged everything into the formula and got

.00008 / .0001 = .08.

Is this the correct answer?
I think I'm doing something wrong here.
The answer is numerically correct, but you might need to give units, which are miles/mile. Note that the cyclist's path is a straight line whose slope can be determined merely by observation. The instantantaneous rate of change of f is going to be the same for all values of x, because the graph of f is straight line.
 

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