Suppose you use a Taylor polynomial with n = 2centered at 0 to approximate a function f. What matching conditions are satisfied by the polynomial?

Solution 1E

Step 1:

Given that

Taylor polynomial with n = 2 centered at 0 to approximate a function f.

Step2:

To find

What matching conditions are satisfied by the polynomial?

Step 3:

The matching conditions are satisfied by the polynomial

In other words, T2 (x) is the polynomial of degree two that has the same function value at x = a, the same first derivative value at x = a, and the same second derivative value at x = a as the original function f(x).