Here is the set of data: $(X,Y)= (1,4.75), (2,4), (3,5.25), (5,19.75), (6,36)$
After I approximated to $3$rd order polynomial with Newton's interpolation, it modeled the true behavior of how $X$ and $Y$ are changing. The rate of change of several slopes has come to $0$ after $3$rd order coefficient. I chose my base point to be close to $4$ to get better accuracy because I was asked to evaluate the function at $4$; the result was $22$. Then I applied Lagrange interpolation and evaluated the $2$nd and $3$rd order polynomial at $4$ but they are straying away from the result I got with Newton's. They were $10.5$ and $10$, respectively. $1$st order matched with Newton's method result, which was $12.5$. What's the reason for this discrepancy? Does that mean Lagrange is not as reliable as Newton's?