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) Since the difference quotient is a difference of fractions divided by h.
2) The numerator 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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