Question

The ordinate of all points on the curve $y=\frac{1}{2 \sin ^2 x+3 \cos ^2 x}$ where the tangent is horizontal, may be

• A. always equal to $1 / 2$
• B. always equal to $1 / 3$
• C. $1 / 2$ or $1 / 3$ according as $n$ is an even or an odd integer.
• D. $1 / 2$ or $1 / 3$ according as $n$ is an odd or an even integer.

Answer 1

Answer: (D)

$y^{\prime}=+\frac{1 \cdot 2 \sin x \cos x}{\left(2+\cos ^2 x\right)^2}=0$
$\sin 2 x=0 $
$x=\frac{n \pi}{2}, n \in I$
if $n$ is odd then $y =\frac{1}{2+\cos ^2 x }=\frac{1}{2} \left(\cos ^2 x =0\right)$ if $n$ is even then $y =\frac{1}{2+\cos ^2 x }=\frac{1}{3} \left(\cos ^2 x =1\right)$