Question 1030987
The area of a certain rectangular pen is given by the formula: 
A(w) = 14w - w^2 ... where w represents the width in feet. 
a) Determine the width that produces the maximum area. 
It's the vertex of the parabola.
A(w) = 14w - w^2
The vertex is on the Axis of Symmetry, w = -b/2a
w = -14/-2 = 7
A(7) = 98 - 49 = 49 sq feet
b) What is the length of the pen (find the area with your answer to part a)?
A(7) = 98 - 49 = 49 sq feet
L = 7 feet, w = 7 feet
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c) Of all rectangles, which particular type gives the maximum area?
A square (for a given perimeter).