find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n$f(x)=4x…

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n$f(x)=4x - 2$\nsimplify your answer as much as possible.\n$\frac{f(x + h)-f(x)}{h}=square$

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n$f(x)=4x - 2$\nsimplify your answer as much as possible.\n$\frac{f(x + h)-f(x)}{h}=square$

Answer

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

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{(4x + 4h-2)-(4x - 2)}{h}\ &=\frac{4x+4h - 2-4x + 2}{h} \end{align*} ]

Step3: Simplify the numerator and then the fraction

The numerator (4x+4h - 2-4x + 2 = 4h). So (\frac{4h}{h}) (since (h\neq0)), and (\frac{4h}{h}=4)

Answer:

(4)