SOLUTION: Please Help. Let {{{f(x)=2x^2-2x}}} Simplify {{{(f(x+h)-f(x))/h}}} Answer: 4x+2h-2 But how? I have tried: {{{(fx+fh)-f(x))/(h)}}} {{{((2x^2-2x)+fh-(2x^2-2x))/h}}} {{{((2

Algebra ->  Functions -> SOLUTION: Please Help. Let {{{f(x)=2x^2-2x}}} Simplify {{{(f(x+h)-f(x))/h}}} Answer: 4x+2h-2 But how? I have tried: {{{(fx+fh)-f(x))/(h)}}} {{{((2x^2-2x)+fh-(2x^2-2x))/h}}} {{{((2      Log On


   

Question 981953: Please Help. Let f%28x%29=2x%5E2-2x
Simplify %28f%28x%2Bh%29-f%28x%29%29%2Fh
Answer: 4x+2h-2
But how? I have tried:
%28fx%2Bfh%29-f%28x%29%29%2F%28h%29
%28%282x%5E2-2x%29%2Bfh-%282x%5E2-2x%29%29%2Fh
%28%282x%5E2-2x%29%2Bfh-2x%5E2%2B2x%29%2Fh
fh%2Fh
Found 3 solutions by josgarithmetic, Edwin McCravy, AnlytcPhil:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You substituted the wrong expression. Try building each part separately before making the substitution into the formula.

f%28x%29=2x%5E2-2x, which already is given.

f%28x%2Bh%29=2%28x%2Bh%29%5E2-2%28x%2Bh%29, the initial x%2Bh input for the function.

Can you take this the rest of the way, into the difference quotient and simplifications... to a final result?

Answer by Edwin McCravy(20056) About Me  (Show Source):
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Question 981953
You are thinking that f(x) means f times x.  
Please get rid of that idea now. f(x) does NOT mean f times x.
The (x) is just a place holder for whatever is going to be
substited for x on the right side of the equation.

Here's an example just like yours that you can go be as a model:

f%28x%29=3x%5E2-4x

Simplify %28f%28x%2Bh%29-f%28x%29%29%2Fh.

Do it in stages.  Find f(x+h), then f(x+h)-f(x), then %28f%28x%2Bh%29-f%28x%29%29%2Fh.


First find f(x+h

f%28x%2Bh%29%22%22=%22%223%28x%2Bh%29%5E2-4%28x%2Bh%29%22%22=%22%223%28x%2Bh%29%28x%2Bh%29-4x-4h%22%22=%22%223%28x%5E2%2B2hx%2Bh%5E2%29-4x-h=3x%5E2%2B6hx%2B3h%5E2-4x-4h 

So

f%28x%2Bh%29%22%22=%22%223x%5E2%2B6hx%2B3h%5E2-4x-4h

and since

%22%22=%22%223x%5E2%2B6hx%2B3h%5E2-4x-4h-%283x%5E2-4x%29%22%22=%22%223x%5E2%2B6hx%2B3h%5E2-4x-4h-3x%5E2%2B4x%22%22=%22%22%22%22=%22%22h%286x%2B3h-4%29%0D%0A%0D%0A%0D%0A

So

f%28x%2Bh%29-f%28x%29%22%22=%22%22h%286x%2B3h-4%29


Then finally find %28f%28x%2Bh%29-f%28x%29%29%2Fh

we divide that by h:

%28f%28x%2Bh%29-f%28x%29%29%2Fh%22%22=%22%22%28h%286x%2B3h-4%29%29%2Fh%22%22=%22%22%28cross%28h%29%286x%2B3h-4%29%29%2Fcross%28h%29%22%22=%22%226x%2B3h-4

So

%28f%28x%2Bh%29-f%28x%29%29%2Fh%22%22=%22%226x%2B3h-4

Edwin