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Thread: Average Rate of Change

  1. #1
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    Average Rate of Change

    For the function given below, answer (a) through (c).

    (a) For each function below, find the average rate of change
    of f from 1 to x:

    [f(x) - f(1)]/(x - 1), where x cannot = 0.

    ==============================

    (b) Use the result from part (a) to compute the average rate of change from x = 1 to x = 2. Be sure to simplify.

    ==============================

    (c) Find an equation of the secant line containing the points
    (1, f(1)) and (2, f(2)).

    HERE IS THE FUNCTION:

    f(x) = x^3 + x
    Last edited by magentarita; Oct 27th 2008 at 07:44 AM. Reason: Added details....
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  2. #2
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    Quote Originally Posted by magentarita View Post
    For the function given below, answer (a) through (c).

    (a) For each function below, find the average rate of change
    of f from 1 to x:

    [f(x) - f(1)]/(x - 1), where x cannot = 0.
    With f(x)= x^3+ x, what is f(1)? Put that into (f(x)- f(1))/(x-1). Once you've done that, you should be able to factor the numerator and cancel.

    ==============================

    (b) Use the result from part (a) to compute the average rate of change from x = 1 to x = 2. Be sure to simplify.
    You are given the formula use it! x= 2 here. What is f(2)? What is f(1)? What is (f(2)- f(1))/(2- 1)? Or just use the formula you got in (a)!

    ==============================

    (c) Find an equation of the secant line containing the points
    (1, f(1)) and (2, f(2)).[
    Presumably by this time you have already calculated the f(1) and f(2) so you know the two points. In (b) you found the slope of this line! How do you find the equation of the line?

    HERE IS THE FUNCTION:

    f(x) = x^3 + x[/QUOTE]
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  3. #3
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    ok..............

    Quote Originally Posted by HallsofIvy View Post
    With f(x)= x^3+ x, what is f(1)? Put that into (f(x)- f(1))/(x-1). Once you've done that, you should be able to factor the numerator and cancel.



    You are given the formula use it! x= 2 here. What is f(2)? What is f(1)? What is (f(2)- f(1))/(2- 1)? Or just use the formula you got in (a)!


    Presumably by this time you have already calculated the f(1) and f(2) so you know the two points. In (b) you found the slope of this line! How do you find the equation of the line?

    HERE IS THE FUNCTION:

    f(x) = x^3 + x
    [/quote]

    I'll play around with this question and hope to understand your steps enough to find the answer.
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