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Local maxima and minima
Last updated at May 29, 2023 by Teachoo
Ex 6.3, 6 Find the maximum profit that a company can make, if the profit function is given by π(π₯) = 41 β 72π₯ β 18π₯2The profit function is given by p(x) = 41 β 72x β 18x2 pβ(x) = β72 β 36 x Putting pβ (x) = 0 β72 β 36x = 0 β36x = 72 π₯ =(β72)/36= β2 Now, Pβ(x) = β36 Since Pβ (x) < 0 π₯=β2 is the maxima β΄ Maximum profit = p(β2) p(x) = 41 β 72x β 18x2 π(β2)=41β72 (β2)β18 (β2)^2 =41+144β18 (4) =41+144β72 =113 Hence, the maximum profit is 113 unit.