Expression 7: "P" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals "f" left parenthesis, "a" , right parenthesis plus "f" prime left parenthesis, "a" , right parenthesis left parenthesis, "x" minus "a" , right parenthesisP1x=fa+f′ax−a
7
Degree 2:
8
Expression 9: "P" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals "f" left parenthesis, "a" , right parenthesis plus "f" prime left parenthesis, "a" , right parenthesis left parenthesis, "x" minus "a" , right parenthesis plus StartFraction, "f" prime prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction left parenthesis, "x" minus "a" , right parenthesis squaredP2x=fa+f′ax−a+f′′a2x−a2
9
Degree 3:
10
Expression 11: "P" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis equals "f" left parenthesis, "a" , right parenthesis plus "f" prime left parenthesis, "a" , right parenthesis left parenthesis, "x" minus "a" , right parenthesis plus StartFraction, "f" prime prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction left parenthesis, "x" minus "a" , right parenthesis squared positive StartFraction, "f" prime prime prime left parenthesis, "a" , right parenthesis Over 6 , EndFraction left parenthesis, "x" minus "a" , right parenthesis cubedP3x=fa+f′ax−a+f′′a2x−a2+f′′′a6x−a3