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150505050505050Find two positive numbers whose sum is 210 and whose product is a maximum.(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)FirstNumber, xSecondNumberProduct, P21060(210 60)0000060921070(210 70) = 98000400210080(210 80)210 9006(06 OI)06100210100 100(210 100)110210 110 110(210 110) =(b) Use a graphing utility to generate additional rows of the table.SecondNumberFirstNumber, xProduct, P120130140150Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.)(c) Write the product P as a function of x(x)d(d) Use a graphing utility to graph the function in part (c).2000000L000150000900L0002000000000-2000000201200011000000010950000109000009000010850000100150200150000000Estimate the solution from the graph.NX(e) Use calculus to find the critical number of the function in part (c). Then find the two numbers.(smaller value)(larger value)

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Find two positive numbers whose sum is 210 and whose product is a maximum.
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
First
Number, x
Second
Number
Product, P
210
60(210 60)
00
0006
09
210
70(210 70) = 9800
04
00
210
0
80(210 80)
210 90
06
(06 OI)06
100
210
100 100(210 100)
110
210 110 110(210 110) =
(b) Use a graphing utility to generate additional rows of the table.
Second
Number
First
Number, x
Product, P
120
130
140
150
Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.)
(c) Write the product P as a function of x
(x)d
(d) Use a graphing utility to graph the function in part (c).
200
0000L
000
150
0009
00L
000
2000
0
000
00
-2000
00
020
12000
11000
0000
10950
000
10900
0009
0000
10850
000
100
150
200
150
000
00
0
Estimate the solution from the graph.
NX
(e) Use calculus to find the critical number of the function in part (c). Then find the two numbers.
(smaller value)
(larger value)
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150 50 50 50 50 50 50 Find two positive numbers whose sum is 210 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Number, x Second Number Product, P 210 60(210 60) 00 0006 09 210 70(210 70) = 9800 04 00 210 0 80(210 80) 210 90 06 (06 OI)06 100 210 100 100(210 100) 110 210 110 110(210 110) = (b) Use a graphing utility to generate additional rows of the table. Second Number First Number, x Product, P 120 130 140 150 Use the table to estimate the solution. (Hint: Use the table feature of the graphing utility.) (c) Write the product P as a function of x (x)d (d) Use a graphing utility to graph the function in part (c). 200 0000L 000 150 0009 00L 000 2000 0 000 00 -2000 00 020 12000 11000 0000 10950 000 10900 0009 0000 10850 000 100 150 200 150 000 00 0 Estimate the solution from the graph. NX (e) Use calculus to find the critical number of the function in part (c). Then find the two numbers. (smaller value) (larger value)

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check_circleAnswer
Step 1

To find two positive numbers whose sum is 210 and whose product is a maximum.

(a) Analytically complete six rows of the given table.

First
Second
Product, P
number, xnumer
60(210-60)9000
70(210 70) 9800
80(210 80) 10400
90(210-90) 10800
210 100 100(210 -100) =11000
210-110 110(210-110) 11000
210-120 120(210 -120) 10800
210-130 130(210 -130) 10400
60
210 60
70
210 70
80
210-80
210-90
90
100
110
120
130
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First Second Product, P number, xnumer 60(210-60)9000 70(210 70) 9800 80(210 80) 10400 90(210-90) 10800 210 100 100(210 -100) =11000 210-110 110(210-110) 11000 210-120 120(210 -120) 10800 210-130 130(210 -130) 10400 60 210 60 70 210 70 80 210-80 210-90 90 100 110 120 130

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Step 2

(b) Use a graphing utility to add the rows and fill it.

First
Second
Product, P
number, x
numer
210-140 140(2 10 -140) 9800
210-150 150(210-150) 9000
210 -160 160(210-160) 8000
210-170 170(210-170) 6800
210 180 180(210-180) 5400
140
150
160
170
180
The estimate solution from the table is x = 100.
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First Second Product, P number, x numer 210-140 140(2 10 -140) 9800 210-150 150(210-150) 9000 210 -160 160(210-160) 8000 210-170 170(210-170) 6800 210 180 180(210-180) 5400 140 150 160 170 180 The estimate solution from the table is x = 100.

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Step 3

(c) To write the product P as a...

P(
=x(210-x
= 2 10x -x'
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P( =x(210-x = 2 10x -x'

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