Which sequence of steps is a correct derivation of the difference quotient for f(x) = 3 – log x?

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          

answer: 5

step-by-step explanation: