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GATE CSE 2012 | Question: 62

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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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B. $10$

$y = 2x - 0.1x^{2}$

$\frac{\mathrm{d} y}{\mathrm{d} x} = 2 - 2\times 0.1x$

$ \frac{\mathrm{d} y}{\mathrm{d} x} =0 \implies x=10$

So, $y= 20-10=10$
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y=2x - 0.1x^2      it's basically an equation of parabola

(x-10)^2 = - 10(y-10)         // it's form of x^2= -4ay  graph will go downward :-

 

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