Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$
A)
$\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 9 } { x ( x + h ) }$
B)
$\frac { f ( x + h ) - f ( x ) } { h } = \frac { 9 } { x + h }$
C)
$\frac { f ( x + h ) - f ( x ) } { h }$ = 9
D)
$\frac { f ( x + h ) - f ( x ) } { h }$ = 1

Question

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$
A) 
$\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 9 } { x ( x + h ) }$
B) 
$\frac { f ( x + h ) - f ( x ) } { h } = \frac { 9 } { x + h }$
C) 
$\frac { f ( x + h ) - f ( x ) } { h }$ = 9
D) 
$\frac { f ( x + h ) - f ( x ) } { h }$ = 1

Quizplus · Accepted Answer

The difference quotient for $f(x) = \frac{9}{x}$ involves substituting $x + h$ into the function, subtracting $f(x)$, and dividing by $h$. The correct simplification leads to $-\frac{9}{x(x+h)}$.

Find the Difference Quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Find the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h }$