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help - derivatives-??

0 votes

asked May 6, 2015 in CALCULUS by anonymous

2 Answers

0 votes

(10)

Step 1:

Perimeter of the three pens is ft

Let each pen has length ft and breadth ft.

Observe the figure:

The total perimeter of the three pens is .

.

Area of the total fencing is image.

Substitute .

.

The area of the rectangular field is always positive.

image and .

image and image.

is  positive on the interval image.

answered May 6, 2015 by Sammi Mentor
0 votes

Contd...

Step 2:

Find the dimensions of the rectangular field, that will enclose the maximum area.

Apply derivative on each side with respect to image.

.

Find the critical numbers by equating image.

image ft.

Substitute image in .

 ft.

The dimensions of the rectangular field are image ft and ft.

answered May 6, 2015 by Sammi Mentor

Contd...

Step 3:

The maximum value of image occurs at either at critical number or at end point of the interval image.

Substitute image in .

image.

Substitute in .

image

image

image

image.

Substitute in .

image

image

image

image

image sq ft.

The maximum area of a rectangular fencing is image sq ft.

Solution:

The dimensions of the each pen are image ft and ft.

The maximum area of a rectangular fencing is image sq ft.

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