The cubic polynomial 
on the interval 
to 
must satisfy four conditions: 
, 
, 
and 
. This uniquely determines the polynomial, leaving no room for the usual requirement that the second derivative should be continuous. To obtain this, you would need quartic splines. John d'Errico's answer and comments to Clay Fulcher's question may be of help. (I do not have the Curve fitting Toolbox so I cannot test this.)
on the interval to must satisfy four conditions: , , and . This uniquely determines the polynomial, leaving no room for the usual requirement that the second derivative should be continuous. To obtain this, you would need quartic splines. John d'Errico's answer and comments to Clay Fulcher's question may be of help. (I do not have the Curve fitting Toolbox so I cannot test this.)
