Q. 85.0( 1 Vote )
Prove that f(x) = sin x + √3 cos x has maximum value at x = π/6.
Answer :
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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