Problema Solution
If 200 feet of fence is to be used to enclose a rectangular pen, the resulting area of the pen is A=w*l=x(100-x), where x is the width of the pen. What is the maximum possible area of the pen?
Answer provided by our tutors
we need to find the maximum of the parabolic function:
f(x) = x(100 - x)
f(x) = -x^2 + 100x
since the quotient in front of x^2 is -1<0 the function has maximum in the vertex:
f max = c - b^2/4a, where a = -1, b = 100, c = 0
f max = 0 - 100^2/(4*(-1))
f max = 2,500 ft^2
the maximum possible area of the pen is 2,500 ft^2.