Question

The point on the curve $y=\cos (x+y),x\in [0,\pi ]$ at which the tangent is parallel to $x+2=0$ is

• A. $(\frac{\pi }{2},0)$
• B. $(-\frac{\pi }{2},0)$
• C. $(\frac{3\pi }{2},0)$
• D. $(-\frac{\pi }{4},\frac{\pi }{4})$

Answer 1

The correct option is B $(-\frac{\pi }{2},0)$

$y=\cos (x+y)$

$\frac{dy}{dx}=-\sin (x+y)(1+\frac{dy}{dx})$

Since slope of tangent $=\infty$

(As slope of $x=2$ is $\infty$)

So, $\frac{dy}{dx}=\infty =\frac{1}{0}$

And $\frac{dy}{dx}=\frac{-\sin (x+y)}{1+\sin (x+y)}=\frac{1}{0}$

So, $\sin (x+y)=-1$

$(x+y)=\frac{3\pi }{2}$ or $-\pi /2$

So, point is $(-\frac{\pi }{2},0)$