let $f(x)=x^{2}-3x - 4$. what is the average rate of change from $x = 7$ to $x = 10$? enter your answer in…

let $f(x)=x^{2}-3x - 4$. what is the average rate of change from $x = 7$ to $x = 10$? enter your answer in the box.

let $f(x)=x^{2}-3x - 4$. what is the average rate of change from $x = 7$ to $x = 10$? enter your answer in the box.

Answer

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, $a = 7$, $b = 10$, and $f(x)=x^{2}-3x - 4$.

Step2: Calculate $f(7)$

Substitute $x = 7$ into $f(x)$: $f(7)=7^{2}-3\times7 - 4=49-21 - 4=24$.

Step3: Calculate $f(10)$

Substitute $x = 10$ into $f(x)$: $f(10)=10^{2}-3\times10 - 4=100-30 - 4=66$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(10)-f(7)}{10 - 7}$, we substitute $f(7) = 24$ and $f(10)=66$: $\frac{66 - 24}{10 - 7}=\frac{42}{3}=14$.

Answer:

14