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GATE ME 2012 | Question: 63

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A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y=2x-0.1x^2$ where $y$ is the height of the arch in meters. The maximum possible height of the arch is

  1. $8$ meters
  2. $10$ meters
  3. $12$ meters
  4. $14$ meters
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y = 2x - 0.1x2 

dy/dx = 2 - 0.2x  

d2y/dx2 = -0.2 

Since, d2y/dx2 < 0 , maximum value of y can be obtained by solving the equation dy/dx = 2 - 0.2x  = 0

2 - 0.2x = 0

2 = 0.2x

Hence, x = 2/0.2 = 10

y = 2x - 0.1x2  = 2(10) - 0.1(10)2 = 20 - 0.1(100) = 20 - 10 = 10

Thus, Answer is B) 10 metres :)

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