. A rain gutter piece isto be made of aluminum sheets that are 20 inches wide and 15 inches long,
by turning up the edges 90°.
a. Write down an equation for the volume of the gutter piece as a function of x.
b. What depth x will provide maximum volume (and hence allows the most water in the
gutter)? Use derivatives!
c. What is the maximal volume?
Now, assume that the aluminum sheets are a inches wide.
d. Determine the maximal volume. Of course, your result will contain the parameter a.
assuming the fold is made on the 20" side,
(a) v = 15x(20-2x) = 300x - 30x^2
(b) dv/dx = 300 - 60x
the rest should be clear. Post your work if you get stuck.