Example
3. Use the
function
and
the point
and
draw the graphs of Newton cubic polynomials with
and compare them with the Taylor
polynomial.
Solution 3.
![[Graphics:../Images/TangentParabolaMod_gr_211.gif]](../Images/TangentParabolaMod_gr_211.gif)
We can graph the secant polynomials
corresponding to
and the Taylor polynomial.
![[Graphics:../Images/TangentParabolaMod_gr_214.gif]](../Images/TangentParabolaMod_gr_214.gif)
![[Graphics:../Images/TangentParabolaMod_gr_217.gif]](../Images/TangentParabolaMod_gr_217.gif)
The next figure shows a comparison of the Taylor polynomial T3(x) and f(x):
![[Graphics:../Images/TangentParabolaMod_gr_220.gif]](../Images/TangentParabolaMod_gr_220.gif)
![[Graphics:../Images/TangentParabolaMod_gr_223.gif]](../Images/TangentParabolaMod_gr_223.gif)
(c) John H. Mathews 2004