Question

Let $f\left(x\right)=\left(sin\right)^{3} x-3sin⁡x+6,\forall x\in \left(0 , \pi \right).$ The number of local maximum/maxima of the function $f\left(\right.x\left.\right)$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

As $f^{'} \left(x\right) = 3 \left(sin\right)^{2} x . cos x - 3 cos x$
$=3cos x\left(\left(sin\right)^{2} ⁡ x - 1\right)$

Hence, $f\left(x\right)$ shows no local maximum.