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MHT CET20244 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If sum of two numbers is 3 , then the maximum value of the product of first number and square of the second number is

Options

  1. A6
  2. B4
  3. C5
  4. D3

Correct answer

B. 4

Step-by-step solution

Let the two numbers be a and b . array ll & a+b=3 & b=3-a...(i) array Product of first number and square of second number (p)=a b^2 p = a (3- a )^2 [ From (i)] array ll & p=9 a-6 a^2+a^3 ...(ii) & d p d a =9-12 a+3 a^2 & d^2 p d a^2 =-12+6 a array Now, dp da =0 3 a ^2-12 a +9=0 aligned & (3 a-9)(a-1)=0 & a=3 or a=1 aligned . d ^2 p d da ^2 |_ a=3 =6 0 and . d ^2 p da ^2 |_ a =1 =-6 0 Maximum value of p is at a =1 Maximum value of the product =4 ...[From (ii)]

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