We consider a rectangular parallelepiped-shaped box based on a rectangle and open from above. The height...

We consider a rectangular parallelepiped-shaped box based on a rectangle and open from above. The height of the box is 4 dm. The base of the box has a fixed perimeter 20 dm and one side of it is x with 0 <x <10.
a. Prove that the total area of the box as a function of x is E(x)=-x²+10x=80, x belongs to (0,10)
b. Find for which value of x the box has a maximum area.
c. Show that E^'[E(X) / 40] <6, for each x belongs to (0,10).
d. Find the value of x for which it holds E(x-2)=absolute value of x-7 + 105.

Expert Solution

milcah answered 2 years ago

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