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Calculus/Pre-Cal.-Evaluating a Difference Quotient.

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Expert: - 9/7/2008


Question
For f(x)=4/x+1, find f(x)-f(15)/x-15

hi there,

  I saw in one of your past tutors who had a similar problem you told him/her that they could use an alternative formula to find the difference quotient. So I used it as well, f(x)-f(a)/x-a, and noticed my problem looks like its already in that formula, but now what? I'm stumped.  

Answer
It looks like all you need to do is put 15 into the function and then put that into {f(x)-f(15)}/(x-15).  It looks like f(15) is  4/16=1/4.

The answer is (f(x)-1/4)/(x-15) where f(x)=4/(x+1).  The top can be reduced to (4/4){4/(x+1)} - {(x+1)/(x+1)}/4 = (15-x)/{4(x+1)}.  
When the denominator is included, it becomes (15-x)/{4(x+1)(x-15)}, which is -1/{4(x-1)}.

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