SOLUTION: Given f(x)=X^2+3 find and simplify the difference quotient [f(x+h)-f(x)]/h I know I need to substitute the different equations and I came up with... (x+h)^2+3-(x^2+3) I am

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Question 1202651: Given f(x)=X^2+3 find and simplify the difference quotient [f(x+h)-f(x)]/h
I know I need to substitute the different equations and I came up with...
(x+h)^2+3-(x^2+3)
I am unaware if this substitution is even right or not but any help solving the problem will be greatly appreciated.

Found 2 solutions by Alan3354, mananth:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Difference quotient of f(x) = %28f%28x%2Bh%29-f%28x%29%29%2Fh
Substitute x with x+h
f%28x%29+=+x%5E2%2B3
We have to find the difference quotient for the function.

f%28x%2Bh%29=+f%28%28x%2Bh%29%5E2%2B3%29
f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+%2B3
%28f%28x%2Bh%29-f%28x%29%29%2Fh= +%28x2+%2B+2xh+%2B+h2+%2B3%29+-+%28x2+%2B3%29%29%2Fh

= %28x%5E2+%2B+2xh+%2B+h%5E2+%2B3+-+x2+-3%29%2Fh
= %282xh+%2B+h%5E2%29%2Fh
= h(2x+h)/h
= 2x+h
Therefore, the difference quotient is 2x + h.