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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 6.3, 13 Find two numbers whose sum is 24 and whose product is as large as possible. Let first number be 𝑥 Now, given that First number + Second number = 24 𝑥 + second number = 24 Second number = 24 – 𝑥 Product = (𝑓𝑖𝑟𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 ) × (𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑢𝑚𝑏𝑒𝑟) = 𝑥 (24−𝑥) Let P(𝑥) = 𝑥 (24−𝑥) We need product as large as possible Hence we need to find maximum value of P(𝑥) Finding P’(x) P(𝑥)=𝑥(24−𝑥) P(𝑥)=24𝑥−𝑥^2 P’(𝑥)=24−2𝑥 P’(𝑥)=2(12−𝑥) Putting P’(𝑥)=0 2(12−𝑥)=0 12 – 𝑥 = 0 𝑥 = 12 Finding P’’(𝑥) P’(𝑥)=24−2𝑥 P’’(𝑥) = 0 – 2 = – 2 Thus, p’’(𝑥) < 0 for 𝑥 = 12 𝑥 = 12 is point of maxima & P(𝑥) is maximum at 𝑥 = 12 Finding maximum P(x) P(𝑥)=𝑥(24−𝑥) Putting 𝑥 = 12 p(12)= 12(24−12) = 12(12) = 144 ∴ First number = x = 12 & Second number = 24 – x = (24 – 12)= 12

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.