Question

find the difference quotient (\frac{f(x + h)-f(x)}{h}) for the function (f(x)=9x - 1). simplify your answer as much as possible.

Explanation:

Step1: Find \( f(x + h) \)

Substitute \( x+h \) into \( f(x)=9x - 1 \).
\( f(x + h)=9(x + h)-1=9x+9h - 1 \)

Step2: Calculate \( f(x + h)-f(x) \)

\( f(x + h)-f(x)=(9x + 9h-1)-(9x - 1) \)
\( =9x+9h - 1-9x + 1=9h \)

Step3: Compute \( \frac{f(x + h)-f(x)}{h} \)

Substitute \( f(x + h)-f(x)=9h \) into \( \frac{f(x + h)-f(x)}{h} \).
\( \frac{f(x + h)-f(x)}{h}=\frac{9h}{h} \)
Since \( h
eq0 \), cancel out \( h \).

Answer:

\( 9 \)