Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-$$f ( x ) = \frac { 1 } { 7 x }$$
A) $\frac { - 1 } { 7 x ( x + h ) }$
B) $\frac { 1 } { 7 x }$
C) 0
D) $\frac { - 1 } { x ( x + h ) }$

Question

Quizplus · Accepted Answer

To find the difference quotient, substitute $f(x) = \frac{1}{7x}$ into the formula: $$\frac{f(x+h)-f(x)}{h} = \frac{\frac{1}{7(x+h)} - \frac{1}{7x}}{h}$$. Simplifying this expression leads to $\frac{-1}{7x(x+h)}$, which matches choice A.

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

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