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in Derivatives by (50.2k points)
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At x = 5π/6, f (x) = 2 sin3x + 3 cos3x is:

A. maximum
B. minimum
C. zero
D. neither maximum nor minimum

1 Answer

+2 votes
by (48.8k points)
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Best 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

⇒ 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.

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