Question

find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function and simplify it.

$f(x)=16x$

the difference quotient is
(simplify your answer. do not factor.)

Explanation:

Step1: Find f(x + h)

Given \(f(x)=16x\), then \(f(x + h)=16(x + h)=16x+16h\)

Step2: Substitute into difference - quotient formula

\(\frac{f(x + h)-f(x)}{h}=\frac{(16x + 16h)-16x}{h}\)

Step3: Simplify the numerator

\((16x + 16h)-16x=16h\), so \(\frac{(16x + 16h)-16x}{h}=\frac{16h}{h}\)

Step4: Cancel out h

\(\frac{16h}{h}=16\)

Answer:

16