Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Minima/ maxima (statement questions) - Number questions
Minima/ maxima (statement questions) - Number questions
Last updated at April 16, 2024 by Teachoo
Ex 6.3, 13 Find two numbers whose sum is 24 and whose product is as large as possible. Let first number be š„ Now, given that First number + Second number = 24 š„ + second number = 24 Second number = 24 ā š„ Product = (šššš š” šš¢šššš ) Ć (š ššššš šš¢šššš) = š„ (24āš„) Let P(š„) = š„ (24āš„) We need product as large as possible Hence we need to find maximum value of P(š„) Finding Pā(x) P(š„)=š„(24āš„) P(š„)=24š„āš„^2 Pā(š„)=24ā2š„ Pā(š„)=2(12āš„) Putting Pā(š„)=0 2(12āš„)=0 12 ā š„ = 0 š„ = 12 Finding Pāā(š„) Pā(š„)=24ā2š„ Pāā(š„) = 0 ā 2 = ā 2 Thus, pāā(š„) < 0 for š„ = 12 š„ = 12 is point of maxima & P(š„) is maximum at š„ = 12 Finding maximum P(x) P(š„)=š„(24āš„) Putting š„ = 12 p(12)= 12(24ā12) = 12(12) = 144 ā“ First number = x = 12 & Second number = 24 ā x = (24 ā 12)= 12