Question

find the difference quotient of f, that is, find (\frac{f(x + h)-f(x)}{h}), (h
eq0), for the following function.
(f(x)=6x + 8)
(\frac{f(x + h)-f(x)}{h}=square) (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute \( x + h \) into \( f(x) = 6x + 8 \), we get \( f(x + h)=6(x + h)+8 = 6x+6h + 8 \).

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

Subtract \( f(x) \) from \( f(x + h) \): \( (6x + 6h+8)-(6x + 8)=6x + 6h+8 - 6x - 8 = 6h \).

Step3: Divide by h

Divide the result by \( h \) (since \( h
eq0 \)): \( \frac{6h}{h}=6 \).

Answer:

\( 6 \)