$$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$$
-$f ( x ) = \frac { 8 } { x ^ { 2 } }$
A) $\frac { - 8 ( 2 a + h ) } { a ^ { 2 } \left( a ^ { 2 } + h \right) }$
B) $\frac { 8 ( 2 a + h ) } { a ^ { 2 } ( a + h ) ^ { 2 } }$
C) $\frac { 8 ( 2 a + h ) } { a ^ { 2 } \left( a ^ { 2 } + h \right) }$
D) $\frac { - 8 ( 2 a + h ) } { a ^ { 2 } ( a + h ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = \frac{8}{x^2}$ simplifies to $\frac{-8(2a+h)}{a^2(a+h)^2}$, which matches choice D. This involves substituting $f(a+h)$ and $f(a)$ into the difference quotient formula, simplifying, and factoring correctly.