For the function f, construct and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h }$
-$f ( x ) = \frac { 16 } { x + 14 }$
A) $- \frac { 224 } { ( x + h + 14 ) ( x + 14 ) }$
B) $- \frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$
C) $- \frac { 16 } { ( x + 16 ) ^ { 2 } }$
D) $\frac { 16 } { ( x + h + 14 ) ( x + 14 ) }$

Question

Quizplus · Accepted Answer

To find the difference quotient, we substitute $f(x) = \frac{16}{x + 14}$ into the formula $\frac{f(x + h) - f(x)}{h}$. This gives us $\frac{\frac{16}{x + h + 14} - \frac{16}{x + 14}}{h}$. Simplifying this expression by finding a common denominator and then dividing by $h$ results in $-\frac{16}{(x + h + 14)(x + 14)}$, which matches choice B.

For the Function F, Construct and Simplify the Difference Quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

For the Function F, Construct and Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h }$