008A Sample Final A, Question 12

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Question: Find and simplify the difference quotient for f(x) =

Foundations
1) f(x + h) = ?
2) How do you eliminate the 'h' in the denominator?
Answer:
1).
2) The numerator of the difference quotient is   so the first step is to simplify this expression. This then allows us to eliminate the 'h' in the denominator.

Solution:

Step 1:
The difference quotient that we want to simplify is
Step 2:
Now we simplify the numerator:
Arithmetic:
Now we simplify the numerator:
Final Answer:

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