I have been tutoring for the last 10 years, privately and for several different companies. I specialize in all things Mathematical, I can tackle low end Chemistry and Physics as well. I have two kids and am currently working for two tutoring labs in the Athens, GA area.
A roofing contractor is fabricating gutters from 12-inch aluminum sheeting. The contractor plans to use an aluminum siding folding press to create the gutter by creasing equal lengths for the sidewalls (see figure).
(a) Let $ x $ represent the height of the sidewall of the gutter. Write a function $ A $ that represents the cross-sectional area of the gutter.
(b) The length of the aluminum sheeting is 16 feet.Write a function $ V $ that represents the volume of one run of gutter in terms of $ x $.
(c) Determine the domain of the function in part (b).
(d) Use a graphing utility to create a table that shows sidewall heights $ x $ and the corresponding volumes $ V $.Use the table to estimate the dimensions that will produce a maximum volume.
(e) Use a graphing utility to graph $ V $. Use the graph to estimate the value of $ x $ for which $ V(x) $ is a maximum. Compare your result with that of part (d).
(f) Would the value of $ x $ change if the aluminum sheeting were of different lengths? Explain.