Question

Y^2=x+sin x no of points at which tangent is parallel to x axis

Answer 1

$y {}^{2} = x + \sin(x) \\ diff \: wrt \: x \\ 2y \frac{dy}{dx} = 1 + cos \: x \\ \frac{dy}{dx} = \: \frac{1 + cos \: x}{2y} \\ for \: tanget \: ll \: to \: x \: axis \\ put \: \frac{dy}{dx} = 0 \\ cos \: x \: = - 1 \\ x = (2n - 1)\pi$