Find and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = \frac { 1 } { 5 x }$$
A) $\frac { 1 } { 5 x }$
B) 0
C) $\frac { - 1 } { x ( x + h ) }$
D) $\frac { - 1 } { 5 x ( x + h ) }$

Question

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = \frac{1}{5x}$ is calculated as follows: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{1}{5(x+h)} - \frac{1}{5x}}{h}$$ Simplifying this expression, we get $\frac{-1}{5x(x+h)}$, which matches option D.

Find 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

Find and Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$