Question $4[20$ marks$]$

Consider the following set of data points in the table below:

$(4\mathrm{.}1)$ Using guidepoints of your choice from the data set, construct the connected Bezier curve

from the set of points.

$($Hint: Divide the set of points into three parts$)$

$(4\mathrm{.}2)$ Draw the connected Bezier polynomial $.$

$(4\mathrm{.}3)$ Why is the graph smoothly connected at points $3$ and $6?$

Manual calculations only. No coding allowed.