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Ex 6.5, 6 - Find maximum profit that a company can make, p(x)

Ex 6.5,6 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Ex 6.5, 6 Find the maximum profit that a company can make, if the profit function is given by 𝑝(π‘₯) = 41 – 72π‘₯ – 18π‘₯2The profit function is given by p(x) = 41 βˆ’ 72x βˆ’ 18x2 p’(x) = βˆ’72 βˆ’ 36 x Putting pβ€˜ (x) = 0 βˆ’72 βˆ’ 36x = 0 βˆ’36x = 72 π‘₯ =(βˆ’72)/36= βˆ’2 Now, P”(x) = βˆ’36 Since P” (x) < 0 π‘₯=βˆ’2 is the maxima ∴ Maximum profit = p(βˆ’2) p(x) = 41 βˆ’ 72x βˆ’ 18x2 𝑝(βˆ’2)=41βˆ’72 (βˆ’2)βˆ’18 (βˆ’2)^2 =41+144βˆ’18 (4) =41+144βˆ’72 =113 Hence, the maximum profit is 113 unit.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.