Question

Find the Taylor series using the first four Taylor polynomial of F(x)  =7x3-6x2+1                                

for x=2.

Answer 1

F(x)=7x³-6x²+1

F(2)=56-24+1=33

F'(x)=21x²-12x

F'(2)=84-24=60

F''(x)=42x-12

F''(2)=84-12=72

F'''(x)=42=F'''(2)

P₄(x)=33+60(x-2)+72(x-2)²/2!+42(x-2)³/3!

P₄(x)=33+60(x-2)+36(x-2)²+7(x-2)³ is the 4-term Taylor polynomial.

P₄(x)≡F(x) when P₄(x) is expanded.