f(x) = sin x + √3 cos x

f’(x) = cos x – √3 sin x

Now,

f’(x) = 0

cos x – √3 sin x = 0

cos x = √3 sin x

cot x = √3

x =

Differentiate f’’(x), we get

f’’(x) = – sin x –√3 cos x

f’’() =

Hence, at x = is the point of local maxima.