Mathematics - Application of Derivative Question with Solution | TestHub

The points of intersection: $x^2=2,y=1$, i.e. $(\pm \sqrt{2},1)$. Here $1<x^2<3$, so the intersecting branches are $y=x^2-1$ and $y=-\left(x^2-3\right)$ At $(\sqrt{2},1):m_1=2x=2\sqrt{2},m_2=-2x=-2\sqrt{2}$ $\therefore \tan \theta =\left|\frac{4\sqrt{2}}{1-8}\right|=\frac{4\sqrt{2}}{7}\Rightarrow \theta ={\tan }^{-1}\left(\frac{4\sqrt{2}}{7}\right)$