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

Quizplus · Accepted Answer

The difference quotient for $f(x) = \frac{9}{x}$ simplifies to $-\frac{9}{x(x+h)}$, which is obtained by substituting $f(x+h) = \frac{9}{x+h}$ and $f(x) = \frac{9}{x}$ into the difference quotient formula and simplifying.

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