# Thread: Applying the difference quotient.

1. ## 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.

2. ## Re: Applying the difference quotient.

Originally Posted by sepoto
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 \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 \displaystyle \begin{align*} \frac{f(t + \Delta t) - f(t)}{\Delta t} \end{align*}, you put \displaystyle \displaystyle \begin{align*} f(t + \Delta t) = 4.4(t + \Delta t) \end{align*} when it should be \displaystyle \displaystyle \begin{align*} 4.4(t + \Delta t)^2 \end{align*}

3. ## 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.

4. ## Re: Applying the difference quotient.

I don't see any further calculations...