Q.Using Lagrange's interpolation formula, find $y$ at $x=2$ given the points $(1,2),(3,10),(4,17)$.

$\text{Term 1: } y_0\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}=2\cdot\frac{(2-3)(2-4)}{(1-3)(1-4)}=2\cdot\frac{(-1)(-2)}{(-2)(-3)}=2\cdot\frac26=\frac23$

$\text{Term 2: } y_1\frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}=10\cdot\frac{(2-1)(2-4)}{(3-1)(3-4)}=10\cdot\frac{(1)(-2)}{(2)(-1)}=10\cdot\frac{-2}{-2}=10$

$\text{Term 3: } y_2\frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}=17\cdot\frac{(2-1)(2-3)}{(4-1)(4-3)}=17\cdot\frac{(1)(-1)}{(3)(1)}=-\frac{17}3$