Question 424413
Solution: Denote the base of the gutter x ft, then the length of the turning up
          will be:
                     {{{(1-x)/2}}} Therefore the shape of gutter is a parallelepiped base rectangle with dimensions x, (1-x)/2 and altitude 5 ft. 

 The volume of the gutter is: {{{V=5*x*(1-x)/2}}}
            
             {{{V=2.5*x-2.5*x^2}}} The graph of this function is 

  a downward parabola and its vertex is the maximum.

   {{{x=(-2.5/-5)=1/2}}} 

   {{{y=2.5*(1/2)-2.5*x^2}}}  y =5/8 cubic feet.

Answer: We need to turn up (1- 1/2)/2= (1/2)/2= 1/4 ft (quoter feet) that the volume of gutter will be maximum: V = 5/8 cubic feet.