# Math Help - Difference Quotient Problem

1. ## Difference Quotient Problem

Hello all,

I have been doing a difference quotient problem for homework and can't seem to get it right.

The problem is this:
Find f(x+h)-f(x)/h where h=/=0 given the function x^2-x+4.

By following my teacher's instructions I did this and got this answer:

However, I am told the problem is wrong, and I have tried doing it several times, and I can't seem to get the correct answer..

Any help would be greatly appreciated. Thank you very much in advance.

Edit:

While looking at the problem I found a place where I made a mistake and I still got the wrong answer having taken that mistake into consideration:

the mistake was where -(x^2-x+4) were concerned the correct way would have been -x^2+x-4 not -x^2-x-4.

After doing that I get the answer 3x+h which is also incorrect.

2. ## Re: Difference Quotient Problem

You reduce to $\frac{h+ h^2}{h}$ and say that that is equal to h. That is your mistake. $\frac{h+ h^2}{h}= \frac{h(1+ h)}{h}= 1+ h$ (for h not equal to 0).

3. ## Re: Difference Quotient Problem

Originally Posted by StaplerPro
Hello all,

I have been doing a difference quotient problem for homework and can't seem to get it right.

The problem is this:
Find f(x+h)-f(x)/h where h=/=0 given the function x^2-x+4.

By following my teacher's instructions I did this and got this answer:

However, I am told the problem is wrong, and I have tried doing it several times, and I can't seem to get the correct answer..

Any help would be greatly appreciated. Thank you very much in advance.

Edit:

While looking at the problem I found a place where I made a mistake and I still got the wrong answer having taken that mistake into consideration:

the mistake was where -(x^2-x+4) were concerned the correct way would have been -x^2+x-4 not -x^2-x-4.

After doing that I get the answer 3x+h which is also incorrect.
The numerator simplifies to 2xh + h^2 - h ....

4. ## Re: Difference Quotient Problem

Thank you for your reply HallsofIvy, I see your logic and it makes sense, however if I put it into the homework problem, I am told that answer is also incorrect.

5. ## Re: Difference Quotient Problem

Mr. fantastic, I did the first part over and I see that you are correct in that, *embarassed*.

Does this mean if I divide it by h the answer would be .. 2x+h? I'm sorry, I'm not very good at this..

6. ## Re: Difference Quotient Problem

Originally Posted by StaplerPro
Mr. fantastic, I did the first part over and I see that you are correct in that, *embarassed*.

Does this mean if I divide it by h the answer would be .. 2x+h? I'm sorry, I'm not very good at this..

(2xh + h^2 - h)/h does NOT equal 2x + h.

7. ## Re: Difference Quotient Problem

Forgive me for asking too many silly questions here..

Let me use a picture to explain what I'm doing (trying another way since 2x+h is incorrect):

? If not then should I divide the h in parenthesis by the h below as well to make it 2x-1?