The function representing the volume of the rectangular prism is given to be:
[tex]V(h)=h(h-5)(h-6)[/tex]Since we are expected to find the volume using the graph, we can prepare a table of values for the function using values of h as integers from 1 - 5, such that:
[tex]\begin{gathered} At\text{ }h=1 \\ V(1)=1(1-5)(1-6)=-4\times-5=20 \end{gathered}[/tex]The completed table is shown below:
Hence, we can plot these points on a graph using a graphing calculator for ease of work. This is shown below:
The maximum volume of the prism is represented by the highest point on the graph. The graph's highest point is at:
[tex]h=1.811[/tex]The corresponding value for the volume as can be seen on the graph is:
[tex]V=24.193[/tex]This is the maximum volume of the prism.
To the nearest cubic foot, the maximum volume of the rectangular prism is 24 cubic feet.
