Given: f(x) = sin X + √3 cos X
To prove: the given function has maximum value at x = π/6
Explanation: given f(x) = sin X + √3 cos X
We will find the first derivative of the given function, we get
Now applying the derivative, we get
f'(x) = cos x-√3sin x
Now critical point is found by equating the first derivative to 0, i.e.,
f’(x) = 0
⇒ cos x-√3sin x = 0
⇒ √3sin x = cos x
Applying the derivative, we get
f’’(x) = -sin x-√3cos x
Now we will substitute x = π/6 in the above equation, we get
f’’(x) = -sin x-√3cos x
Hence proved
