Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = \frac { 13 } { x + 26 }$$
A) $- \frac { 13 } { ( x + 13 ) ^ { 2 } }$
B) $- \frac { 338 } { ( x + h + 26 ) ( x + 26 ) }$
C) $\frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$
D) $- \frac { 13 } { ( x + h + 26 ) ( x + 26 ) }$

Question

Quizplus · Accepted Answer

The difference quotient for $f(x) = \frac{13}{x + 26}$ is calculated as follows: $\frac{f(x + h) - f(x)}{h} = \frac{\frac{13}{x + h + 26} - \frac{13}{x + 26}}{h}$. Simplifying this expression leads to $- \frac{13}{(x + h + 26)(x + 26)}$, which matches choice D.

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

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