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Answer 1 · 2017-10-20T10:24:18

The maximum capacity is obtained by bending the metal sheet at #6cm# from the edge.

If the length of the sheet is #L=24# and the bends are done at distance #h# from the edge, the section of the gutter is:

#S= h xx (24-2h) = 24h-2h^2#

To find the maximum value of #S# differentiate with respect to #h#:

#(dS)/(dh) = d/(dh) (24h-2h^2) = 24-4h#

and find critical points with the equation:

#(dS)/(dh) = 0#

#24-4h = 0#

#h=6#

As: #(d^2S)/(dh^2) = -4 < 0# any critical point is a local maximum.

Thus the maximum capacity is obtained by bending the metal sheet at #6cm# from the edge.