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
⇒ f' (x)=2.cos3x.3-3.sin3x.3
⇒ f’(x)=6cos3x-9sin3x……(i)
Now we will find the value of f’(x) at x = 5π/6, we get
And we find that f’(x) at x = 5π/6 is not equal to 0.
So x = 5π/6 cannot be point of maxima or minima.
Hence, f (x) = 2 sin3x + 3 cos3x at x = 5π/6 is neither maxima nor minima.
So the correct option is option D.