63. Victor Klee's Endpoint Maximum Problem Given 40 m of straight fence, your goal is to build a rectangular enclosure using 80 additional meters of fence that encompasses the greatest area. Let A(x) be the area of the enclosure, with x as in Figure 31. (a) Find the maximum value of A(x). (b) Which interval of x values is relevant to our problem? Find the maximum value of A(x) on this interval. 40 20-x 20 -x 40+x FIGURE 31

Question
63. Victor Klee's Endpoint Maximum Problem Given 40 m of straight fence, your goal is to build a rectangular
enclosure using 80 additional meters of fence that encompasses the greatest area. Let A(x) be the area of the enclosure,
with x as in Figure 31.
(a) Find the maximum value of A(x).
(b) Which interval of x values is relevant to our problem? Find the maximum value of A(x) on this interval.
40
20-x
20 -x
40+x
FIGURE 31
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Transcribed Image Text

63. Victor Klee's Endpoint Maximum Problem Given 40 m of straight fence, your goal is to build a rectangular enclosure using 80 additional meters of fence that encompasses the greatest area. Let A(x) be the area of the enclosure, with x as in Figure 31. (a) Find the maximum value of A(x). (b) Which interval of x values is relevant to our problem? Find the maximum value of A(x) on this interval. 40 20-x 20 -x 40+x FIGURE 31

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