Symmetric Matrices & Quadratic Forms · Medium problem

The Rayleigh quotient of a symmetric matrix $A$ at a nonzero vector $\mathbf v$ is $R(\mathbf v) = \dfrac{\mathbf v^{T}A\mathbf v}{\mathbf v^{T}\mathbf v}$. For $A = \begin{pmatrix}4 & 2\\2 & 1\end{pmatrix}$ and $\mathbf v = \begin{pmatrix}1\\1\end{pmatrix}$, compute $R(\mathbf v)$.