A rectangle ABCD is inscribed in the area between the x-axis and the part of the graph of y = cos(4x) between its x-intercepts (see diagram).

[NeedMathHelp12345]

A rectangle ABCD is inscribed in the area between the x-axis and the part of the graph of y = cos(4x) between its x-intercepts (see diagram). (a) Determine the function that models the perimeter of ABCD as a function of x. (b) Determine the maximum perimeter of ABCD and the dimensions of this rectangle of maximum perimeter.

I don't even know where to start with this.

 

[Deleted member 4993]

A rectangle ABCD is inscribed in the area between the x-axis and the part of the graph of y = cos(4x) between its x-intercepts (see diagram). (a) Determine the function that models the perimeter of ABCD as a function of x. (b) Determine the maximum perimeter of ABCD and the dimensions of this rectangle of maximum perimeter.

I don't even know where to start with this. View attachment 27664

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Dr.Peterson]

A rectangle ABCD is inscribed in the area between the x-axis and the part of the graph of y = cos(4x) between its x-intercepts (see diagram). (a) Determine the function that models the perimeter of ABCD as a function of x. (b) Determine the maximum perimeter of ABCD and the dimensions of this rectangle of maximum perimeter.

I don't even know where to start with this. View attachment 27664

Here's a place to start:

Suppose D is at x=X, and A is at x=-X. What are the coordinates of B and C? Then, write an expression for the perimeter of ABCD, as a function of X. (I wish they hadn't said "as a function of x", because x is not a fixed number in the picture.)

Do that, show us what you've done, and then think about part (b).

 

[pka]

Look at this plot. Now consider only part of the perimeter of ABCD along the \(x-\)axis & in the first quadrant.
If \(D\) is \((t,0)\) then is that part of the perimeter \(2t+\cos(4t)~?\)
What is the whole perimeter of ABCD? How does one maximize its length?