find the average rate of change of f(x)= - 5x + 4 from 4 to 12. the average rate of change of f(x)= - 5x + 4…
find the average rate of change of f(x)= - 5x + 4 from 4 to 12. the average rate of change of f(x)= - 5x + 4 from 4 to 12 is (simplify your answer.)
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, $a = 4$, $b=12$, and $f(x)=-5x + 4$.
Step2: Calculate $f(12)$
Substitute $x = 12$ into $f(x)$: $f(12)=-5\times12 + 4=-60 + 4=-56$.
Step3: Calculate $f(4)$
Substitute $x = 4$ into $f(x)$: $f(4)=-5\times4+4=-20 + 4=-16$.
Step4: Calculate the average rate of change
$\frac{f(12)-f(4)}{12 - 4}=\frac{-56-(-16)}{12 - 4}=\frac{-56 + 16}{8}=\frac{-40}{8}=-5$.
Answer:
$-5$