微積分 應(yīng)用題
A rain gutter is to be constructed from a length of sheet metal that is 24cm wide.To form the gutter,the width is folded along its
length,in three equal sections,so that both ends form an angle @ with the middle section (horizontal).Find the angle that will
maximize the capacity of the rain gutter.
a) Since the capacity is proportional to the cross-sectional area created by the folds,find the cross-sectional area as a function of
the angle.
b) Give a reasonable explanation of why the set of possible angles should be a clased set.
c) Carry out the optimization to find the angle that maximizes the capacity of the gutter.