# Difference Quotient

• Feb 1st 2009, 04:17 PM
usrnme14
Difference Quotient
Hello,

I am having a hard time understanding the difference quotient.
f(x+h)-f(x)
-----------
h

Ex: for f(x)= 8x+9

I understand that for every x, I put in 8x+9 for it, but what do i do for the first part where it is f(x+h)? Here is where I get confused. In some examples from school it becomes (x+h)^2 . How is that possible if you are supposed to plug in 8x+9 for every x? I dont get it.

Other problems I'm having trouble with
f(x)= 5x^2
f(x)= x^2+3x+9

I'm sure with a detailed explanation, i can solve these.

Thanks for yalls help
• Feb 1st 2009, 04:21 PM
Jhevon
Quote:

Originally Posted by usrnme14
Hello,

I am having a hard time understanding the difference quotient.
f(x+h)-f(x)
-----------
h

Ex: for f(x)= 8x+9

I understand that for every x, I put in 8x+9 for it, but what do i do for the first part where it is f(x+h)? Here is where I get confused. In some examples from school it becomes (x+h)^2 . How is that possible if you are supposed to plug in 8x+9 for every x? I dont get it.

apparently you don't understand :p

to find f(x + h) you replace all the x's in f(x) with x + h.

if \$\displaystyle f({\color{red}x}) = 8{\color{red}x} + 9\$, then \$\displaystyle f({\color{red}x + h}) = 8({\color{red}x + h}) + 9 = 8x + 8h + 9\$

now, you know f(x) and f(x + h), so just plug them into the difference quotient formula.

Quote:

Other problems I'm having trouble with
f(x)= 5x^2
f(x)= x^2+3x+9

I'm sure with a detailed explanation, i can solve these.

Thanks for yalls help
try these yourself. post what you get
• Feb 1st 2009, 05:25 PM
usrnme14
I'm Lost
I still don't get it. I'm not understanding how you got that. Could you post a solution and how you got it to just one of the problems, so i can follow it?

Thanks,
• Feb 2nd 2009, 09:32 AM
Jhevon
Quote:

Originally Posted by usrnme14
I still don't get it. I'm not understanding how you got that. Could you post a solution and how you got it to just one of the problems, so i can follow it?

Thanks,

how i got what? i even color coded it. all you do is wherever you see "x", you write "(x + h)" instead. that is it

f(x)........................f(x + h)

8x -----------------> 8(x + h)

9x -----------------> 9(x + h)

x^2 ---------------> (x + h)^2

2x^2 + 3x + 2 ----> 2(x + h)^2 + 3(x + h) + 2

is this really that confusing? why don't you try? you might pleasantly surprise yourself