find the average rate of change for f(x) = x² - 3x - 10 from x = 4 to x = 6. a 5 b 7 c 9 d 11

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 6$, and $f(x)=x^{2}-3x - 10$.

Step2: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=4^{2}-3\times4 - 10=16-12 - 10=-6$.

Step3: Calculate $f(6)$

Substitute $x = 6$ into $f(x)$: $f(6)=6^{2}-3\times6 - 10=36-18 - 10=8$.

Step4: Calculate the average rate of change

$\frac{f(6)-f(4)}{6 - 4}=\frac{8-(-6)}{2}=\frac{8 + 6}{2}=\frac{14}{2}=7$.

Answer:

B. 7