Expand the following expression in the difference quotient and simplify. $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0 . \quad f ( x ) = \frac { 5 } { 2 x }$$
A) $\frac { 5 } { 2 \left( x ^ { 2 } + h \right) }$
B) $- \frac { 5 } { 2 ( x + h ) ^ { 2 } }$
C) $- \frac { 5 } { 2 x ( x + h ) }$
D) $\frac { 5 } { 2 ( x + h ) }$
E) $- \frac { h } { x ( x + h ) }$

Question

Quizplus · Accepted Answer

The difference quotient for $f(x) = \frac{5}{2x}$ is calculated as follows: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{5}{2(x+h)} - \frac{5}{2x}}{h} = \frac{5(2x) - 5(2(x+h))}{2x(2(x+h))h} = -\frac{5h}{2x(x+h)h} = -\frac{5}{2x(x+h)}.$$ This simplifies to option C.

Expand the Following Expression in the Difference Quotient and Simplify f(x+h)−f(x)h,h≠0.f(x)=52x\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0 . \quad f ( x ) = \frac { 5 } { 2 x }hf(x+h)−f(x)​,h=0.f(x)=2x5​

Expand the Following Expression in the Difference Quotient and Simplify $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0 . \quad f ( x ) = \frac { 5 } { 2 x }$