Question

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h
eq0$, for the function below.
$f(x)=4x - 2$
simplify your answer as much as possible.
$\frac{f(x + h)-f(x)}{h}=square$

Explanation:

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

Given \(f(x)=4x - 2\), then \(f(x + h)=4(x + h)-2=4x+4h - 2\)

Step2: Substitute into the difference quotient formula

$$
LATEXBLOCK0
$$

Step3: Simplify the numerator and then the fraction

The numerator \(4x+4h - 2-4x + 2 = 4h\). So \(\frac{4h}{h}\) (since \(h
eq0\)), and \(\frac{4h}{h}=4\)

Answer:

\(4\)