# 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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Which is the result help_outlineImage Transcriptionclose150 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) fullscreen

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