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
A. 8 meters
B. 10 meters
C. 12 meters
D. 14 meters
GATE 2012 · General Aptitude · Maxima Minima · medium
Answer: Maximum height = 10 meters. Answer: B. 10 meters
Differentiate the arch equation: Taking the derivative of y = 2x - 0.1x^2 term by term: d/dx(2x) = 2 and d/dx(-0.1x^2) = -0.2x.
Set derivative to zero and solve for x: The critical point is at x = 10. Since d^2y/dx^2 = -0.2 < 0, this is indeed a maximum.
Substitute x = 10 back to find maximum height: The maximum height of the arch is 10 meters.