The maximum value of f ( x )= sin x (1+ cos x ) is

Question

The maximum value of f ( x )= sin x (1+ cos x ) is (A) (3 √3/4) (B) (3 √3/2) (C) 3 √3 (D) √3

Tardigrade Admin · Accepted Answer

Θ f(x)= sin x(1+ cos x)= sin x+( sin 2 x/2) ⇒ f prime( x )= cos x + cos 2 x =2 cos 2 x + cos x -1=( cos x +1)(2 cos x -1) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ee1eb029a51eaaf90580ca992b8dcc81-.png" /> ∴ f ( x ) is maximum at x =(π/3) ∴ f ((π/3))=(√3/2)(1+(1/2))=(3 √3/4)

Q. The maximum value of $f (x) = sin x (1 + cos x)$ is

$\frac{3 3}{4}$

$\frac{3 3}{2}$

$33$

$3$

$Θ f (x) = sin x (1 + cos x) = sin x + \frac{s i n 2 x}{2}$
$\Rightarrow f^{'} (x) = cos x + cos 2 x = 2 cos^{2} x + cos x - 1 = (cos x + 1) (2 cos x - 1)$

$∴ f (x)$ is maximum at $x = \frac{π}{3}$
$∴ f (\frac{π}{3}) = \frac{3}{2} (1 + \frac{1}{2}) = \frac{3 3}{4}$

Q. The maximum value of f(x)=sinx(1+cosx) is

433​​

233​​

33​

3​

Θf(x)=sinx(1+cosx)=sinx+2sin2x​ ⇒f′(x)=cosx+cos2x=2cos2x+cosx−1=(cosx+1)(2cosx−1) ∴f(x) is maximum at x=3π​ ∴f(3π​)=23​​(1+21​)=433​​

Q. The maximum value of $f (x) = sin x (1 + cos x)$ is

$\frac{3 3}{4}$

$\frac{3 3}{2}$

$33$

$3$

$Θ f (x) = sin x (1 + cos x) = sin x + \frac{s i n 2 x}{2}$
$\Rightarrow f^{'} (x) = cos x + cos 2 x = 2 cos^{2} x + cos x - 1 = (cos x + 1) (2 cos x - 1)$

$∴ f (x)$ is maximum at $x = \frac{π}{3}$
$∴ f (\frac{π}{3}) = \frac{3}{2} (1 + \frac{1}{2}) = \frac{3 3}{4}$