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

Question

Accepted Answer

**Setting up the three terms** ($x_0=1,y_0=2$; $x_1=3,y_1=10$; $x_2=4,y_2=17$; evaluating at $x=2$)

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

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

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

**Summing** …

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

Concept understanding — Lagrange's Interpolation Formula

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

Concept understanding — Lagrange's Interpolation Formula

🎓Unlock everything free for 14 days

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

Unlock everything free for 14 days