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Homework Help: Difference quotient problems

  1. Sep 15, 2014 #1
    1. The problem statement, all variables and given/known data
    Find f(a), f(a + h),and the difference quotient f(a + h) − f(a), h where h ≠ 0.

    f(x) = 5x/x-1

    f(a) = ?
    f(a + h) = ?
    f(a + h) − f(a)/(h) = ?

    3. The attempt at a solution

    As I understand it I must substitute the values but I don't understand the question. say if it were something like 1/x I would know to fill it into (1/(x+h)-1/x) / h
    But this just confuses me I don't know how to answer these questions
  2. jcsd
  3. Sep 15, 2014 #2

    Ray Vickson

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    The way you wrote it you have
    [tex] f(x) = \frac{5x}{x} - 1 = 5 - 1 = 4 [/tex]
    so ##f(a) = f(a+h) = 4##. Perhaps you really did not mean what you wrote, but because you failed to use parentheses it is impossible to say. And, of course, you wrote
    [tex]f(a+h) - \frac{f(a)}{h} = 4 - \frac{4}{h}. [/tex]
    Again, maybe you meant something different.
  4. Sep 15, 2014 #3
    What I meant was: f(x) = (5x)/(x-1) my mistake
  5. Sep 17, 2014 #4


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    Just replace every instance of x with the given value. Where the given value consists of an expression, like a+h, put the expression in parentheses when making the substitution.
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