find the average rate of change of f(x)=x² + x - 3 on the interval -2,1:

Answer:

0

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, $a=-2$, $b = 1$, and $f(x)=x^{2}+x - 3$.

Step2: Calculate $f(a)$

Substitute $x=-2$ into $f(x)$: $f(-2)=(-2)^{2}+(-2)-3=4 - 2-3=-1$.

Step3: Calculate $f(b)$

Substitute $x = 1$ into $f(x)$: $f(1)=1^{2}+1-3=1 + 1-3=-1$.

Step4: Calculate the average rate of change

$\frac{f(1)-f(-2)}{1-(-2)}=\frac{-1-(-1)}{1 + 2}=\frac{-1 + 1}{3}=0$.