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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 - 0.1$$x^{2}$

$dy/dx=2 - 2$*$0.1$ $x =>$ $dy/dx=0 =>$ $x=10$

So, $y= 20-10=10$
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Why dy/dx is 0?

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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