Find the difference quotient of $$ f $$, that is, find $$ \frac{f(x+h)-f(x)}{h}, h
eq 0 $$, for the following function. $$ f(x)=-4 x+6 $$

Question

Find the difference quotient of $$ f $$, that is, find $$ \frac{f(x+h)-f(x)}{h}, h 
eq 0 $$, for the following function. $$ f(x)=-4 x+6 $$

UpStudy AI · Accepted Answer

To find the **difference quotient** of the function $$ f(x) = -4x + 6 $$, we use the formula:

$$
\frac{f(x+h) - f(x)}{h}, \quad h \neq 0
$$

**Step 1: Compute $$ f(x+h) $$**

$$
f(x+h) = -4(x + h) + 6 = -4x - 4h + 6
$$

**Step 2: Compute $$ f(x+h) - f(x) $$**

$$
f(x+h) - f(x) = (-4x - 4h + 6) - (-4x + 6) = -4h
$$

**Step 3: Divide by $$ h $$**

$$
\frac{f(x+h) - f(x)}{h} = \frac{-4h}{h} = -4 \quad \text{(since $$ h \neq 0 $$)}
$$

**Conclusion:**

The difference quotient of the function $$ f(x) = -4x + 6 $$ is:

$$
\frac{f(x+h) - f(x)}{h} = -4
$$
The difference quotient of $$ f(x) = -4x + 6 $$ is $$-4$$.

Find the difference quotient of \( f \), that is, find \( \frac{f(x+h)-f(x)}{h}, h \neq 0 \), for the following function. \( f(x)=-4 x+6 \)