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Math Help - Rational function

  1. #1
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    Rational function

    What do you mean by this?

    Find  \frac{f(x+h)-f(x)}{h} for:

     f(x)=3x^2-4x+1


    Can you explain me what is this problem? thanks!
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  2. #2
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    Quote Originally Posted by Anemori View Post
    What do you mean by this?

    Find  \frac{f(x+h)-f(x)}{h} for:

     f(x)=3x^2-4x+1


    Can you explain me what is this problem? thanks!
    Hi

    In this case

     \frac{f(x+h)-f(x)}{h} = \frac{(3(x+h)^2-4(x+h)+1)-(3x^2-4x+1)}{h}

    Expand and simplify
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi

    In this case

     \frac{f(x+h)-f(x)}{h} = \frac{(3(x+h)^2-4(x+h)+1)-(3x^2-4x+1)}{h}

    Expand and simplify

    This is what i get:

    6x+3h-4


    now my problem is how to graph f(x) and its difference quotient in same window..... hmmm.....

    pls help,,, thanks!
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  4. #4
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    Quote Originally Posted by Anemori View Post
    This is what i get:

    6x+3h-4
    That is correct

    Quote Originally Posted by Anemori View Post
    now my problem is how to graph f(x) and its difference quotient in same window..... hmmm.....
    You cannot graph the difference quotient unless you give a value to h (otherwise you have 2 variables : x and h)

    Usually when you have to compute \frac{f(x+h)-f(x)}{h} you make h go to 0 (as an introduction to the derivatives), which gives 6x-4
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  5. #5
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    Quote Originally Posted by running-gag View Post
    That is correct

    You cannot graph the difference quotient unless you give a value to h (otherwise you have 2 variables : x and h)

    Usually when you have to compute \frac{f(x+h)-f(x)}{h} you make h go to 0 (as an introduction to the derivatives), which gives 6x-4

    Here is the instruction for graphing it:

    Graph f(x) and its difference quotient by hand in the same window. Provide all relevant work regarding the vertex, axis symmetry, etc.

    True or false? The root of difference quotient when h=0 is the x-coordinate of the minimum of f(x).


    I guess it says i have to graph it with h=0.
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