Q8 of 137 Page 18

Prove that f(x) = sin x + √3 cos x has maximum value at x = π/6.

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.


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