APPLICATION OF CONTINUITY OF A FUNCTION

Question

A rectangular garden will be placed adjacent to a building. It will be enclosed by wooden fences using 125 feet of material such that the building will be considered as a boundary on one of the garden’s side. If x feet is the side of the garden perpendicular to the building, express the area in square feet of the garden in terms of x. What is the domain of this function? Show that the function is continuous within its domain.

Answer 1

area = x(125-2x) = 125x -2x^2

A(x) = 125x -2x^2

, 2x<125, x<62.5

0<x<62.5

the domain is between 0 and 62.5

the area = zero, when x=0 or 62.5

the area, A(x), is graphically a downward opening parabola with x intercepts (0, 0) and (62.5, 0), vertex (31.25, 1953.25) Maximum area is 1,953.25 ft^2, when x=31.25 feet and the side parallel to the building is 62.5 feet

The area can be any real number between zero and 1,953.25 ft^2, as x varies between zero and 62.5 feet