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This is Maximum when x is ?

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To find the maximum, I would use calculus. if you don't know calculus, then you should graph this on a graphing calculator or using graph paper & find the highest point on the graph.
 
Using calculus:
 
y = 3^.5 * sin x + cos x
 
y' = 3^.5 * cos x - sin x
 
3^.5 * cos x - sin x = 0
 
3^.5 * cos x = sin x
 
3^.5 = tan x
 
x = pi/3 & 4pi/3
 
When pi/3 is put into the original equation, the answer is positive. However, the answer is negative when 4pi/3 is put in. The maximum would have to be at pi/3
 
y = 3^.5 * sin (pi/3) + cos (pi/3) = (3^.5)(3^.5)/2 + 1/2 = 3/2 + 1/2 = 2