Question

given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=4x - 2$ answer

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$:
$f(x + h)=4(x + h)-2=4x+4h - 2$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(4x + 4h-2)-(4x - 2)$
$=4x+4h - 2-4x + 2=4h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{4h}{h}=4$

Answer:

$4$