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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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)

Image Transcription

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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