Question

find and simplify the difference quotient for the given function F(x)=1/8x? can anyone tell me how can I apply F(a+h)-f(a)/h formula to this question?

Answer 1

\[\frac{F(a+h)-f(a)}{h}=\frac{\dfrac{1}{8(a+h)}-\dfrac{1}{8a}}{h}\]
Combine the fractions in the numerator:
\[\frac{\dfrac{\color{red}a}{8\color{red}a(a+h)}-\dfrac{\color{red}{a+h}}{8a(\color{red}{a+h})}}{h}\]
\[\frac{\dfrac{a-(a+h)}{8a(a+h)}}{h}\]
and so on.