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Diana has available 520 yards of fencing and wishes to enclose a rectangular area.(a) Express the area A of the rectangle as a function of the width W of the rectangle.(b) For what value of W has the area largest?(c) What is the maximum area?

Question

Diana has available 520 yards of fencing and wishes to enclose a rectangular area.

(a) Express the area A of the rectangle as a function of the width W of the rectangle.

(b) For what value of W has the area largest?

(c) What is the maximum area?

 

check_circleAnswer
Step 1

a). 

Perimeter of a rectangle = P = 2(1+w)
P 212w
21 P-2w
Р
=-w
2
. Area of a rectangle A =lxw
Р
ww
Р
-w-w
2
help_outline

Image Transcriptionclose

Perimeter of a rectangle = P = 2(1+w) P 212w 21 P-2w Р =-w 2 . Area of a rectangle A =lxw Р ww Р -w-w 2

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Step 2

b). The area is largest at the point where its derivative is zero.

       now differentiating area with respect to w, we get

dAP2w
dw 2
dA
=0 gives
Now
P
-2w 0
2
Р
2w
2
Р
W
help_outline

Image Transcriptionclose

dAP2w dw 2 dA =0 gives Now P -2w 0 2 Р 2w 2 Р W

fullscreen
Step 3

Hence, area is largest when the...

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Calculus

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