Question

Suppose you have 74 feet of fencing to enclose a rectangular dog pen. The function a=37x-x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary

Answer 1

Answer: width = 18.5 ft; area = 342.3 ft2

Explanation:

you plug in the width with the function , where ever there is an x replace it with the width for the maximum area

Answer 2

The function is that of a parabola. You can tell because it has the;
Standard form: ax² + bx + c
Given equation: -x² + 37x + 0

Since the "a" coefficient is negative, the parabola is flipped upside down making the maximum point the vertex.

Vertex = (-b/2a, y)
-b/2a = -37/(-1*2) = 37/2 = 18.5
This is the x-value, width which gives the maximum area

put in x = 18.5 and solve for maximum area, A.
A = -(18.5)² + 37(18.5)
A = -342.25 + 684.5
A = 342.25
round to nearest tenth
A = 342.3