the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=3x + 1$

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: $f(x + h)=3(x + h)+1=3x+3h + 1$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(3x+3h + 1)-(3x + 1)$ $=3x+3h + 1-3x - 1=3h$

Step3: Find the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{3h}{h}=3$

Answer:

$3$