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

Question

Let f(x)=(sin)3 x-3sin⁡x+6,∀ x∈ (0 , π ). The number of local maximum/maxima of the function f(.x.) is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

As f' (x) = 3 (sin)2 x . cos x - 3 cos x =3cos x((sin)2 ⁡ x - 1) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-fedue8h0wrk7.png" /> Hence, f(x) shows no local maximum.

Q. Let $f (x) = (s in)^{3} x - 3 s in x + 6, \forall x \in (0, π) .$ The number of local maximum/maxima of the function $f (x)$ is

$0$

$1$

$2$

$3$

As $f^{^{'}} (x) = 3 (s in)^{2} x . cos x - 3 cos x$
$= 3 cos x ((s in)^{2} x - 1)$

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

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

0

1

2

3

As f′(x)=3(sin)2x.cosx−3cosx =3cosx((sin)2⁡x−1) Hence, f(x) shows no local maximum.

Q. Let $f (x) = (s in)^{3} x - 3 s in x + 6, \forall x \in (0, π) .$ The number of local maximum/maxima of the function $f (x)$ is

$0$

$1$

$2$

$3$

As $f^{^{'}} (x) = 3 (s in)^{2} x . cos x - 3 cos x$
$= 3 cos x ((s in)^{2} x - 1)$

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