let f(x)=x² - 3x - 4. what is the average rate of change from x = 7 to x = 10? enter your answer in the box.
let f(x)=x² - 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 $f(10)$
Substitute $x = 10$ into $f(x)$: $f(10)=10^{2}-3\times10 - 4=100-30 - 4=66$.
Step3: Calculate $f(7)$
Substitute $x = 7$ into $f(x)$: $f(7)=7^{2}-3\times7 - 4=49-21 - 4=24$.
Step4: Calculate the average rate of change
$\frac{f(10)-f(7)}{10 - 7}=\frac{66 - 24}{3}=\frac{42}{3}=14$.
Answer:
14