$$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$$
-$f ( x ) = \frac { 4 } { x }$
A) $\frac { 4 } { a }$
B) $\frac { - 1 } { 4 a ( a + h ) }$
C) $\frac { - 4 } { a ( a + h ) }$
D) $\frac { - 4 } { a }$

Question

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = \frac{4}{x}$ is calculated as follows: $\frac{f(a+h)-f(a)}{h} = \frac{\frac{4}{a+h} - \frac{4}{a}}{h}$. Simplifying this expression leads to $\frac{-4}{a(a+h)}$, which matches choice C.