Question

4b. approximately which value of x will give elena a box with the greatest volume?
elena graphs the volume of the box along with the function ( b(x)=140 ).

Explanation:

Step1: Analyze the graph of \(y = V(x)\)

The function \(y = V(x)\) represents the volume of the box. To find the value of \(x\) that gives the greatest volume, we need to find the \(x -\) coordinate of the local maximum of the function \(y = V(x)\).

Step2: Locate the local maximum on the graph

Looking at the graph of \(y = V(x)\), we observe the peak (local maximum) of the curve. By visual inspection of the graph (assuming standard \(x -\) axis scaling), the \(x -\) value at the local maximum of \(y = V(x)\) is approximately \(x = 4\).

Answer:

The value of \(x\) that gives the greatest volume is approximately \(x = 4\).