find the average rate of change for $f(x)=x^{2}-8x + 15$ from $x = 0$ to $x = 4$.\na -2\nb -4\nc 2\nd 4
find the average rate of change for $f(x)=x^{2}-8x + 15$ from $x = 0$ to $x = 4$.\na -2\nb -4\nc 2\nd 4
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, $a = 0$, $b = 4$, and $f(x)=x^{2}-8x + 15$.
Step2: Calculate $f(0)$
Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}-8\times0 + 15=15$.
Step3: Calculate $f(4)$
Substitute $x = 4$ into $f(x)$: $f(4)=4^{2}-8\times4 + 15=16-32 + 15=-1$.
Step4: Calculate the average rate of change
$\frac{f(4)-f(0)}{4 - 0}=\frac{-1 - 15}{4}=\frac{-16}{4}=-4$.
Answer:
B. -4