Question

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

Answer 1

B

Explanation:

I guessed and got it right.

Answer 2

Explanation:

Where are the answer choices?

Still, it's possible to help you without your having shared those choices.

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