for the function f(x) = 2x + 1, evaluate and simplify the difference quotient.
for the function f(x) = 2x + 1, evaluate and simplify the difference quotient.
Answer
Explanation:
Step1: Recall difference - quotient formula
The difference quotient of a function $y = f(x)$ is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$.
Step2: Find $f(x + h)$
Given $f(x)=2x + 1$, then $f(x + h)=2(x + h)+1=2x+2h + 1$.
Step3: Substitute into difference - quotient formula
$\frac{f(x + h)-f(x)}{h}=\frac{(2x + 2h+1)-(2x + 1)}{h}$.
Step4: Simplify the numerator
$(2x + 2h+1)-(2x + 1)=2x+2h + 1-2x - 1=2h$.
Step5: Simplify the fraction
$\frac{2h}{h}=2$.
Answer:
$2$