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Word Problem ! Beginning Calculus

  1. Jul 8, 2009 #1


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    1. The problem statement, all variables and given/known data[/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

    2. Relevant equations

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

    3. 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.
  2. jcsd
  3. Jul 8, 2009 #2
    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.
  4. Jul 8, 2009 #3


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    Science Advisor
    Homework Helper

    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?
  5. Jul 8, 2009 #4


    Staff: Mentor

    Make that "where x and f(x) are measured in miles."
    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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