2 a cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5…

2 a cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5, height by x - 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate? 1) 1,2 2) 1,3.5 3) 1,5 4) 0,3.5

2 a cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5, height by x - 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate? 1) 1,2 2) 1,3.5 3) 1,5 4) 0,3.5

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = V(x)$ over the interval $[a,b]$ is given by $\frac{V(b)-V(a)}{b - a}$.

Step2: Calculate for interval [1,2]

From the graph, assume $V(1)=0$ and $V(2)$ is approximately $6$. Then the average rate of change is $\frac{V(2)-V(1)}{2 - 1}=\frac{6 - 0}{1}=6$.

Step3: Calculate for interval [1,3.5]

Assume $V(1) = 0$ and $V(3.5)$ is approximately $18$. Then the average rate of change is $\frac{V(3.5)-V(1)}{3.5 - 1}=\frac{18-0}{2.5}=7.2$.

Step4: Calculate for interval [1,5]

Assume $V(1)=0$ and $V(5)=0$. Then the average rate of change is $\frac{V(5)-V(1)}{5 - 1}=\frac{0 - 0}{4}=0$.

Step5: Calculate for interval [0,3.5]

Assume $V(0)$ is approximately $- 4$ and $V(3.5)$ is approximately $18$. Then the average rate of change is $\frac{V(3.5)-V(0)}{3.5 - 0}=\frac{18+4}{3.5}=\frac{22}{3.5}\approx6.29$.

Answer:

  1. $[1,3.5]$