SOLUTION: what is the difference quotient of -6x^2+7x+4??

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Question 356853: what is the difference quotient of -6x^2+7x+4??
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

Some books use "Dx" and some use "h" to find the difference quotient.
I will use "h".  If your book uses "Dx" then 

f%28x%29+=+-6x%5E2%2B7x%2B4

Difference quotient = %28f%28x%2Bh%29-f%28x%29%29%2Fh

First find the term on the upper left f%28x%2Bh%29 and simplify:

f%28x%2Bh%29+=+-6%28x%2Bh%29%5E2%2B7%28x%2Bh%29%2B4
f%28x%2Bh%29+=+-6%28x%2Bh%29%28x%2Bh%29%2B7x%2B7h%2B4
f%28x%2Bh%29+=+-6%28x%5E2%2B2hx%2Bh%5E2%29%2B7x%2B7h%2B4
f%28x%2Bh%29+=+-6x%5E2-12hx-6h%5E2%2B7x%2B7h%2B4

Substitute %28-6x%5E2-12hx-6h%5E2%2B7x%2B7h%2B4%29 for f%28x%2Bh%29 and %28-6x%5E2%2B7x%2B4%29 for f%28x%29 in
 
%28f%28x%2Bh%29-f%28x%29%29%2Fh

%28%28-6x%5E2-12hx-6h%5E2%2B7x%2B7h%2B4%29-%28-6x%5E2%2B7x%2B4%29%29%2Fh

Remove parentheses:

%28-6x%5E2-12hx-6h%5E2%2B7x%2B7h%2B4%2B6x%5E2-7x-4%29%2Fh

Cancel what will cancel:



%28-12hx-6h%5E2%2B7h%29%2Fh

Factor h out of the top:

%28h%28-12x-6h%2B7%29%29%2Fh

Cancel the h's

%28cross%28h%29%28-12x-6h%2B7%29%29%2Fcross%28h%29

-12x-6h%2B7

Edwin