Finding difference quotients of functions

[Katez]

How do you find the difference quotients of functions?
My textbook doesn't explain it, the teacher didn't go over it (she's a little airheaded) and I have a test Thursday. D=

Sample equation:

Find the difference quotient and simplify your answer.

f(x)= x² - x + 1

f(2 + h) - f(2) h =/=0
___________
h

 

[mmm4444bot]

Please use the [ code ] tags, if you want to "draw" stuff in your posts. (Use the [Preview] button to proofread.)

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



  f(2 + h) - f(2)             h<>0
___________________

        h

Or, just type it, using grouping symbols.

[f(2 + h) - f(2)]/h

All that you need to do is simplify this algebraic ratio. Just because this particular ratio is called a difference quotient, the simplification process is not different from the steps you've used when simplifying other algebraic ratios that you've done in the past.

Well, the first step is to determine the expressions for f(2 + h) and f(2).

If you can't find f(2), then perhaps you're a little air-headed, too. :wink:

f(2 + h) is obtained by substituting the expression 2 + h for x in the definition for function f. (Does this ring any bells?)

After you find f(2 + h) and f(2), subtract the latter from the former, just like it shows in the numerator of the difference quotient.

Factor out an h.

That factor cancels with the h in the denominator.

You're done.

If you want more help with this, then please show whatever work that you can, OR explain what you're thinking, so that we might determine why you're stuck or where to continue.

 

[Katez]

The reason I didn't post any work was because I had absolutely no idea how to do it, so:

Thank you for your help.