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Math Help - Difference quotient

  1. #1
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    Difference quotient

    Using the conjecture that d/dx*x^n=nx^n-1 for positive integer values of n. In this problem we look at negative values of n instead.

    Let f(x)= x^-1.

    (a) write the difference quotient for f(x).

    (b) Let the change of x= .01. Use the table command on your calculator to build a table of values for the difference quotient.

    -Compare the values in your table to the values of -1*x^-2. Can you guess what f'(x) might be based on your table of values?

    x diff quotient -1*x^(-2)
    -4
    -2
    -1
    -1/2
    -1/3

    I am not sure how to go about this problem is the difference quotient for part a d/dx*x^-1=nx^-1-1?

    If someone can help me understand the quotient I am suppose to use and ow i Use it in part b I think I can figure out the table on my own.
    I know the difference quotient how do i use the equation with the d variable or do i even use it?
    Last edited by asweet1; September 17th 2009 at 07:12 PM. Reason: more info
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  2. #2
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    Quote Originally Posted by asweet1 View Post
    Using the conjecture that d/dx*x^n=nx^n-1 for positive integer values of n. In this problem we look at negative values of n instead.

    Let f(x)= x^-1.

    (a) write the difference quotient for f(x).

    (b) Let the change of x= .01. Use the table command on your calculator to build a table of values for the difference quotient.

    -Compare the values in your table to the values of -1*x^-2. Can you guess what f'(x) might be based on your table of values?

    x diff quotient -1*x^(-2)
    -4
    -2
    -1
    -1/2
    -1/3

    I am not sure how to go about this problem is the difference quotient for part a d/dx*x^-1=nx^-1-1?

    If someone can help me understand the quotient I am suppose to use and ow i Use it in part b I think I can figure out the table on my own.
    difference quotient ...

    \frac{f(x + \Delta x) - f(x)}{(x+\Delta x) - x}
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  3. #3
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    I know the difference quotient but my question is if i use the equation with the d variable in these problems?
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  4. #4
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    Quote Originally Posted by asweet1 View Post
    I know the difference quotient but my question is if i use the equation with the d variable in these problems?
    no ... you're only confirming that the conjecture works with negative values of n.
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