Find and simplify the difference quotient $$\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = \frac { 6 } { x }$$
A) $\frac { - 1 } { 6 a ( a + h ) }$
B) $\frac { 6 } { a }$
C) $\frac { - 6 } { a ( a + h ) }$
D) $\frac { - 6 } { a }$

Question

Quizplus · Accepted Answer

To find the difference quotient for $f(x) = \frac{6}{x}$, we substitute $f(a+h)$ and $f(a)$ into the difference quotient formula. This gives us $\frac{\frac{6}{a+h} - \frac{6}{a}}{h}$. Simplifying this expression, we get $\frac{-6}{a(a+h)}$, which matches choice C.

Find and Simplify the Difference Quotient f(a+h)−f(a)h,h≠0\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0hf(a+h)−f(a)​,h=0

Find and Simplify the Difference Quotient $\frac { f ( a + h ) - f ( a ) } { h } , h \neq 0$