Question

for the function f(x) = 3x - 6, construct and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$. the difference quotient for f(x)=3x - 6 is

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x):
$f(x + h)=3(x + h)-6=3x+3h - 6$

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

$f(x + h)-f(x)=(3x + 3h-6)-(3x - 6)$
$=3x+3h - 6-3x + 6=3h$

Step3: Calculate the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{3h}{h}=3$

Answer:

3