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