what is the average rate of change of the function $f(x)=2x + 1$ on the interval $0,1$

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 1$, and $f(x)=2x + 1$.

Step2: Calculate $f(1)$ and $f(0)$

First, find $f(1)$: Substitute $x = 1$ into $f(x)=2x + 1$, then $f(1)=2\times1+1=3$. Next, find $f(0)$: Substitute $x = 0$ into $f(x)=2x + 1$, then $f(0)=2\times0+1 = 1$.

Step3: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, substitute $a = 0$, $b = 1$, $f(1)=3$, and $f(0)=1$: $\frac{f(1)-f(0)}{1 - 0}=\frac{3 - 1}{1}=2$.

Answer:

2