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