Find the difference quotient for the function $$ f(x)=-10 x+2 $$, and simplify it.

Question

UpStudy AI · Accepted Answer

To find the difference quotient for the function $$ f(x) = -10x + 2 $$, follow these steps:

1. **Define the Difference Quotient:**
   
   The difference quotient is given by:
   $$
   \frac{f(x + h) - f(x)}{h}
   $$

2. **Compute $$ f(x + h) $$:**
   
   Substitute $$ x + h $$ into the function:
   $$
   f(x + h) = -10(x + h) + 2 = -10x - 10h + 2
   $$

3. **Subtract $$ f(x) $$ from $$ f(x + h) $$:**
   
   $$
   f(x + h) - f(x) = (-10x - 10h + 2) - (-10x + 2) = -10h
   $$

4. **Divide by $$ h $$:**
   
   $$
   \frac{f(x + h) - f(x)}{h} = \frac{-10h}{h} = -10 \quad \text{(for } h \neq 0\text{)}
   $$

**Simplified Difference Quotient:**
$$
-10
$$
The difference quotient for the function $$ f(x) = -10x + 2 $$ simplifies to $$-10$$.

Find the difference quotient for the function \( f(x)=-10 x+2 \), and simplify it.