Asked by Moses
Find the difference quotient f(x+h)-f(x)/h, where h cannot be equal to 0 , for the function below.
f(x)=1/x+9
Simplify your answer as much as possible.
f(x)=1/x+9
Simplify your answer as much as possible.
Answers
Answered by
Steve
If that is 1/(x+9), then just plug and chug:
f(x+h)-f(x) = 1/(x+h+9) - 1/(x+9)
= [(x+9)-(x+h+9)]/[(x+h+9)(x+9)]
= (-h)/[(x+h+9)(x+9)]
That is the difference. The difference quitient is just that divided by h, so it is
-1/[(x+h+9)(x+9)]
f(x+h)-f(x) = 1/(x+h+9) - 1/(x+9)
= [(x+9)-(x+h+9)]/[(x+h+9)(x+9)]
= (-h)/[(x+h+9)(x+9)]
That is the difference. The difference quitient is just that divided by h, so it is
-1/[(x+h+9)(x+9)]
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