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 |

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

Answer:

$x = 3$

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here $b = 7$, and we need to find $a$ such that $\frac{f(7)-f(a)}{7 - a}=56$.

Step2: Substitute values for different $a$ values

Let's start checking for each $x$ value in the table. If $a = 3$: We know $f(7)=192$ and $f(3)=12$. Then $\frac{f(7)-f(3)}{7 - 3}=\frac{192 - 12}{4}=\frac{180}{4}=45$. If $a = 4$: $f(7)=192$ and $f(4)=24$. Then $\frac{f(7)-f(4)}{7 - 4}=\frac{192 - 24}{3}=\frac{168}{3}=56$. So the $x$ - value is $4$.