1. CONSTRUCTION A roofing contractor is fabricating gutters from 12-inch aluminum sheeting. The…

1. CONSTRUCTION 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 represent the height of
the sidewall of the gutter. Write a function that represents the cross-sectional
area of the gutter.

(b) The length of the aluminum
sheeting is 16 feet. Write a function that represents the volume of one run of
gutter in terms of

(c) Determine the domain of the
function in part (b).

(d) Use a graphing utility to
create a

1. CONSTRUCTION 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 represent the height of
the sidewall of the gutter. Write a function that represents the cross-sectional
area of the gutter.

(b) The length of the aluminum
sheeting is 16 feet. Write a function that represents the volume of one run of
gutter in terms of

(c) Determine the domain of the
function in part (b).

(d) Use a graphing utility to
create a table that shows sidewall heights and the corresponding volumes Use
the table to estimate the dimensions that will produce a maximum volume.

(e) Use a graphing utility to
graph Use the graph to estimate the value of for which is a maximum. Compare
your result with that of part (d).

(f) Would the value of change if
the aluminium sheeting were of different lengths? Explain.

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