Let f x = sin 3 ⁡ x - 3 sin ⁡ x + 6 , ∀ x ∈ 0 , π . The number of local maximum/maxima of the function f ( x ) is

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Question: Answered & Verified by Expert

Let

f (x) = \sin^{3} x - 3 \sin x + 6, \forall x \in (0, π) .

The number of local maximum/maxima of the function

f (x)

is

MathematicsApplication of DerivativesJEE Main

Options:

A $0$
B $1$
C $2$
D $3$

Solution:

1663 Upvotes Verified Answer

The correct answer is:

0

As

f^{'} (x) = 3 \sin^{2} x . \cos x - 3 \cos x

= 3 \cos x (\sin^{2} x - 1)

Hence,

f (x)

shows no local maximum.

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