Question

A rectangle is inscribed in the region bounded by the x-axis, the y-axis, and the graph of x+2y-8=0. Unfortunately, I cant draw the diagram of the graph and the shaded box region, but on the x-axis, the width 4 and on the y-axis, the length 2.
(a) Write the area A of the rectangle as a function of x. Determine the domain of the function in the context of the problem.
(b) Use the table feature of a graphing utility to create a table showing possible values of x and the corresponding areas of the rectangle. Use the table to estimate the dimensions that will produce the maximum area.

Answer 1

(c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce a maximum area.
(d) Write the area function in standard form to find algebraically the dimensions that will produce a maximum area.
(e) Compare your results from parts (b),(c), and (d).

Answer 2

please help me

Answer 3

https://www.desmos.com/calculator/awprgkhdf5

Answer 4

I am not sure why they have max area on this one, since it is using a line so there is no variability to it. Here is a video of one where it shows variability:
http://www.youtube.com/watch?v=3D7hVooFkRI

Where as yours, well, you have a pretty normal triangle so the \(A=\dfrac{bh}{2}\) formula works very nicely. About all you might do is use something to evaluate where y is maximized to get h and x is maximized to get b. Then sub those in.

Answer 5

it says that the area is a= x(8-x/2). I just don't understand how they got that

Answer 6

Well, half the base times the height. So the /2 part is the half. That means x and 8-x are base and height or height and base. You would need to determine which was which.

Answer 7

Ah, I see where I made a mistake. It says rectangle... I was thinking triangle. Doh. OK. So the /2 in this case is because of the areas that would not be used.

Answer 8

A few examples.