Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = \frac { 3 } { x + 28 }$$
A) $- \frac { 3 } { ( x + h + 28 ) ( x + 28 ) }$
B) $- \frac { 84 } { ( x + h + 28 ) ( x + 28 ) }$
C) $- \frac { 3 } { ( x + 3 ) ^ { 2 } }$
D) $\frac { 3 } { ( x + h + 28 ) ( x + 28 ) }$

Question

Quizplus · Accepted Answer

To find the difference quotient, we substitute $f(x) = \frac{3}{x+28}$ into the formula: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{3}{x+h+28}-\frac{3}{x+28}}{h}.$$ Simplifying the expression inside the numerator gives us: $$\frac{3(x+28)-3(x+h+28)}{(x+h+28)(x+28)} = \frac{3x+84-3x-3h-84}{(x+h+28)(x+28)} = -\frac{3h}{(x+h+28)(x+28)}.$$ Dividing by $h$ (and since $h \neq 0$), we get: $$-\frac{3}{(x+h+28)(x+28)}.$$ This matches choice A.

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 $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$