Answer :

Given f (x) = 2 sin3x + 3 cos3x


Applying the first derivative we get



Applying the sum rule of differentiation and taking out the constant terms, we get



Applying the derivative,



f' (x)=2.cos3x.3-3.sin3x.3


f’(x)=6cos3x-9sin3x……(i)


Now we will find the value of f’(x) at , we get




Now split



Now we know cos(2π+θ)=cosθ and sin(2π+θ)=sinθ



Now we know and



And we find that f’(x) at is not equal to 0.


So cannot be point of maxima or minima.


Hence, f (x) = 2 sin3x + 3 cos3x at is neither maxima nor minima.


So the correct option is option D.

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