Find and simplify the difference quotient for the function
.
2

4

Ask by Graham Kelly. in the United States

Jan 22,2025

Question

Find and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ for the function $$ f(x)=2 x+1 $$. 2 $$ 2 x+1 $$ $$ \frac{2 h+2}{h} $$ 4

UpStudy AI · Accepted Answer

To find and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ for the function $$ f(x) = 2x + 1 $$, follow these steps:

1. **Compute $$ f(x + h) $$:**
   $$
   f(x + h) = 2(x + h) + 1 = 2x + 2h + 1
   $$

2. **Find $$ f(x + h) - f(x) $$:**
   $$
   f(x + h) - f(x) = (2x + 2h + 1) - (2x + 1) = 2h
   $$

3. **Divide by $$ h $$ to get the difference quotient:**
   $$
   \frac{f(x + h) - f(x)}{h} = \frac{2h}{h} = 2
   $$

**Final Answer:**  
$$ 2 $$
The difference quotient simplifies to 2.

Find and simplify the difference quotient for the function
.
2

4