Question

find the difference quotient of f; that is, find \\( \frac { f ( x + h ) - f ( x ) } { h } \\), \\( h \
eq 0 \\), for the following function.
\\( f ( x ) = 8 x + 8 \\)
\\( \frac { f ( x + h ) - f ( x ) } { h } = \square \\) (simplify your answer.)

Explanation:

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

Substitute \( x+h \) into \( f(x)=8x + 8 \).
\( f(x + h)=8(x + h)+8=8x+8h + 8 \)

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

\( f(x + h)-f(x)=(8x+8h + 8)-(8x + 8) \)

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

Substitute \( f(x + h)-f(x)=8h \) into \( \frac{f(x + h)-f(x)}{h} \).
\( \frac{f(x + h)-f(x)}{h}=\frac{8h}{h} \)
Since \( h
eq0 \), cancel out \( h \).

Answer:

\( 8 \)