Question

What is the difference quotient for the function f(x) = 8/ 4x + 1

Answer 1

Answer:

Last option (counting from the top)

Step-by-step explanation:

For a given function f(x), the difference quotient is:

$\frac{f(x + h) - f(x)}{h} = \frac{1}{h}*(f(x + h) - f(x))$

In this case, we have:

$f(x) = \frac{8}{4x + 1}$

Then the difference quotient will be:

$\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1})$

Now we should get a common denominator.

We can do that by multiplying and dividing each fraction by the denominator of the other fraction, so we will get:

$\frac{1}{h}*( \frac{8}{4*(x + h) + 1} - \frac{8}{4x + 1}) = \frac{1}{h}*(\frac{8*(4x + 1)}{(4(x + h) +1 )*(4x + 1)} - \frac{8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)})$

Now we can simplify that to get:

$\frac{1}{h}*\frac{8*(4x + 1) - 8*(4(x + h) + 1)}{(4(x + h) +1 )*(4x + 1)}} = \frac{1}{h}*\frac{-32h}{(4(x + h) +1 )*(4x + 1)}} = \frac{-32}{(4(x + h) +1 )*(4x + 1)}}$

Then the correct option is the last one (counting from the top)