question: compute the difference quotient $\\frac{f(x + h)-f(x)}{h}$ for the function given below $f(x)=3x…
question: compute the difference quotient $\\frac{f(x + h)-f(x)}{h}$ for the function given below $f(x)=3x - 5$. select the correct answer below: $3$, $3x - 5$, $3h+3x - 5$, $3x + 3$, $- 5$, $3$
Answer
Explanation:
Step1: Find f(x + h)
Given (f(x)=3x - 5), then (f(x + h)=3(x + h)-5=3x+3h - 5).
Step2: Calculate f(x + h)-f(x)
(f(x + h)-f(x)=(3x + 3h-5)-(3x - 5)=3x+3h - 5-3x + 5=3h).
Step3: Compute the difference - quotient
(\frac{f(x + h)-f(x)}{h}=\frac{3h}{h}=3).
Answer:
3