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Your sister wants to construct a rectangular garden with three separate areas for the two of...

Your sister wants to construct a rectangular garden with three separate areas for the two of you and your brother. She has 400 ft of fencing for the outer boundary and the separating fences. She asks you to calculate the dimensions in order to have the maximum enclosed total area.

(a) Find the total enclosed area, A(x), as a function of the width, x, and determine the x-interval over which it is to be maximized.

(b) Find the critical point of A(x).

(c) Use the second derivative test to check whether the critical point from part (b) is a local maximum.

(d) Use the zeroth derivative test to find the dimensions that maximize the area.

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