Answer:
Step-by-step explanation:
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The "difference quotient" is defined as:
f(x + h) - f(x)
--------------------
h
where h represents an incremental (small) change in x.
Here f(x) = 3 - log x, and so f(x + h) = 3 - log (x + h).
Therefore the difference quotient is:
{3 - log (x + h)} - {3 - log x}
-------------------------------------
h
This can be simplified. In the numerator we have 3 - 3, so the numerator simplifies to -log (x + h) + log x
and the difference quotient is
-log ( x + h) + log x
---------------------------
h
This can be rewritten as
log x - log (x + h) x x
--------------------------- , or (1/h)*log ------------ , or (1/h) log { ----------- }
h (x + h) x + h
