Question

A wire 24inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x:
Determine the domain of the function and use a graphing utility to graph the function over that domain
Use the graph of the function to approximate the maximum area of the rectangle. Make a conjecture about the dimensions that yield a maximum area.

Answer 1

If the function is the Area, then Area = length*width = x*(12-x) = 12x - x^2
Domain is x>0, since you can't have a rectangle with negative length

Answer 2

since it says shortest side, is there a limit to the domain, like is it in an interval?

Answer 3

oh yeah, 0 < x<6, If x is 7 then width would be 5, but x must be shorter

Answer 4

oh okay thank you and i was wondering if you had any idea how to do the next part?

Answer 5

well do you have a graphing calculator or you can use...graphcalc.com
to see what 12x - x^2 looks like

Answer 6

look at the graph , and wherever the graph is highest is the maximum area

Answer 7

i'm not very familiar with the graphing calc. i'm sorry once i graph it is going up continually

Answer 8

change the window size...this is a parabola it will reach a maximum and then start going down

Answer 9

could you possibly try? i'm getting a linear graph which is really absurd..