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Math Help - Applying the difference quotient.

  1. #1
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    Applying the difference quotient.

    f(x) = 4.4t2

    Apply the difference quotient formula:

    f(t - ∆t) – f(t) / ∆t

    4.4(t + ∆t) –(4.4t2) / ∆t

    Somehow the equation above is supposed to reduce to 8.8t however I don’t see how yet. I used an online derivative calculator which shows 8.8t as the answer however what I am being asked to do is apply the difference quotient formula I think to the equation.

    I worked the equation to:

    4.4t2+4.4∆t2+-4.4t2 / ∆t = 4.4∆t

    However I think I must be in error because the answer by the derivative calculator is 8.8t. I need to see how the difference quotient is used because my class did not teach the power rule so I am supposed to apply the difference quotient I believe.
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  2. #2
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    Re: Applying the difference quotient.

    Quote Originally Posted by sepoto View Post
    f(x) = 4.4t2

    Apply the difference quotient formula:

    f(t + ∆t) – f(t) / ∆t

    4.4(t + ∆t) –(4.4t2) / ∆t

    Somehow the equation above is supposed to reduce to 8.8t however I don’t see how yet. I used an online derivative calculator which shows 8.8t as the answer however what I am being asked to do is apply the difference quotient formula I think to the equation.

    I worked the equation to:

    4.4t2+4.4∆t2+-4.4t2 / ∆t = 4.4∆t
    There's no way it could possibly be that. As a general rule, when you have a difference quotient formed by a polynomial, you need to get a common factor of \displaystyle \begin{align*} \Delta t \end{align*} so that it can cancel with the one on the bottom and then be able to be taken to 0.

    For starters, when you did \displaystyle \begin{align*} \frac{f(t + \Delta t) - f(t)}{\Delta t} \end{align*}, you put \displaystyle \begin{align*} f(t + \Delta t) = 4.4(t + \Delta t) \end{align*} when it should be \displaystyle \begin{align*} 4.4(t + \Delta t)^2  \end{align*}
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    Re: Applying the difference quotient.

    I am only asking to see the steps to finding the derivative using the difference quotient formula. I have tried many times to use the difference quotient formula to calculate the derivative and I have not gotten the right answer yet. Yes you are correct I forgot to place the power of 2 on the first part of the formula but if you see in the calculations further I did them as if it would have been there.
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  4. #4
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    Re: Applying the difference quotient.

    I don't see any further calculations...
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