select the correct location on the image. on the interval x, 7, at which x - value is the average rate of…
select the correct location on the image. on the interval x, 7, at which x - value is the average rate of change 56?\n|x|3|4|5|6|7|\n|f(x)|12|24|28|96|192|
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $b = 7$, $a=x$, and the average rate of change is 56, so $\frac{f(7)-f(x)}{7 - x}=56$.
Step2: Substitute values from the table
We know $f(7)=192$. Let's test each $x$ - value from the table. For $x = 3$: $\frac{f(7)-f(3)}{7 - 3}=\frac{192 - 12}{4}=\frac{180}{4}=45$. For $x = 4$: $\frac{f(7)-f(4)}{7 - 4}=\frac{192 - 24}{3}=\frac{168}{3}=56$. For $x = 5$: $\frac{f(7)-f(5)}{7 - 5}=\frac{192 - 28}{2}=\frac{164}{2}=82$. For $x = 6$: $\frac{f(7)-f(6)}{7 - 6}=\frac{192 - 96}{1}=96$.
Answer:
4