Answer :

Given: f(x) = sin X + √3 cos X


To prove: the given function has maximum value at


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




This is possible only when


Now the second derivative of the function is



Applying the derivative, we get


f’’(x) = -sin x-√3cos x


Now we will substitute in the above equation, we get


f’’(x) = -sin x-√3cos x



Substituting the corresponding value, we get





Hence f(x) has maximum value at .


Hence proved


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