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MHT CET202120 Sep 2021Morning ShiftMathematicsApplication of DerivativesActual

A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is

Options

  1. A5
  2. B75
  3. C15
  4. D70

Correct answer

B. 75

Step-by-step solution

Let x be the one part and y be the other part. We have x + y =20 y =20- x As per condition given, we write aligned & f ( x )=(20- x ) x ^3 & =20 x ^3- x ^4 & f ^ ( x )=60 x ^2-4 x ^3 aligned When f ^ ( x ) , we get aligned & 4 x^2(15-x)=0 x=0,15 & f^ (x)=120 x-12 x^2 & [f^ (x) ]_ x=15 =(120)(15)-(12)(15)^2=-900 < 0 aligned f [ x ] is maximum when x =15 . y =5 xy =(15)(5)=75

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