Problema Solution
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A=26x-x^2, 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 provided by our tutors
we need to find the maximum of the parabolic function A = 26x - x^2
A max = c - (b^2)/(4a), where a = -1, b = 26 and c = 0
A max = 0 - (26^2)/(4*(-1))
A max = 169 ft^2
the maximum area is 169 ft^2
by solving 26x - x^2 = 169 we find the maximum width
x = 13 ft
click here to see the step by step solution of the quadratic equation
the width of 13 feet gives the maximum area.