The dimensions of a piece of paper used to wrap a rectangular package are x and 2x−1inches. What is the function with the dimensions that result in the maximum area for the wrapping paper?

Question

Determine the type of function--exponential, linear, or quadratic-- that is most appropriate to model the situation described. Then, use the chosen function model to complete the problem.

Answer 1

This is an area of a rectangle problem.

The area of a rectangle is length * width. both length and width are given in terms of x,

thus the area of the wrapper = x(2x-1)

When we distribute the x we end up with a quadratic function. I will leave it to you to do the distribution, and find the area increases as the value of x increases. I suspect you are missing a constraint such as the total area of the wrapper. Without such a constraint the area will increase without bound.