24. if f(x)=x² - 3x, what is the average rate of change over 0,2? a. 1 b. 2 c. -2 d. -1

Answer:

D. -1

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 2$, and $f(x)=x^{2}-3x$.

Step2: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2^{2}-3\times2=4 - 6=-2$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}-3\times0 = 0$.

Step4: Calculate the average rate of change

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