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 + 3 \\) \\( \frac { f ( x + h ) - f ( x ) } { h } = \square \\) (simplify your answer.)

Explanation:

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

Given \( f(x)=8x + 3 \), then \( f(x + h)=8(x + h)+3=8x+8h + 3 \)

Step2: Substitute \( f(x + h) \) and \( f(x) \) into the difference quotient formula

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Step3: Simplify the numerator and then the fraction

The numerator \(8x+8h + 3-8x - 3 = 8h\). So \(\frac{8h}{h}=8\)

Answer:

\(8\)