Question

compute and completely simplify the difference quotient, $\frac{f(x + h)-f(x)}{h}$, for $f(x)=5x + 5$. give your answer in expanded form.

Explanation:

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

Given \(f(x)=5x + 5\), then \(f(x + h)=5(x + h)+5=5x+5h + 5\)

Step2: Substitute into difference - quotient formula

\(\frac{f(x + h)-f(x)}{h}=\frac{(5x + 5h+5)-(5x + 5)}{h}\)

Step3: Simplify the numerator

\((5x + 5h+5)-(5x + 5)=5x+5h + 5-5x - 5=5h\)

Step4: Simplify the fraction

\(\frac{5h}{h}=5\)

Answer:

5