SOLUTION: How do I determine the difference quotient (simplify when possible)? g(x) = x^2

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Question 1095036: How do I determine the difference quotient (simplify when possible)?
g(x) = x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First compute g(x+h):

g%28x%29+=+x%5E2

g%28x%2Bh%29+=+%28x%2Bh%29%5E2 Replace every x with x+h

g%28x%2Bh%29+=+%28x%2Bh%29%28x%2Bh%29

g%28x%2Bh%29+=+x%28x%2Bh%29%2Bh%28x%2Bh%29

g%28x%2Bh%29+=+x%5E2%2Bxh%2Bxh%2Bh%5E2

g%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2

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Now find the Difference Quotient:

%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28x%5E2%2B2xh%2Bh%5E2+-+x%5E2%29%2Fh

%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%282xh%2Bh%5E2%29%2Fh Note how the x^2 terms subtract and cancel

%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28h%282x%2Bh%29%29%2Fh Factor out the GCF h

%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28cross%28h%29%282x%2Bh%29%29%2F%28cross%28h%29%29 Divide the h terms and cancel

%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+2x%2Bh Simplify

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So when everything is fully simplified, the final answer is 2x%2Bh