Search 72,496 tutors
FIND TUTORS
Ask a question
0 0

Please help me with this problem?

If f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2, then which of the following is the third order Taylor polynomial generated by f(x) at x=0? 
 
a) 2x^3+x
b) (1/3)x^3+(1/2)x
c) (2/3)x^3+x
d) 2x^3-x
e) (1/3)x^3+x
 
Please show all your work. 
Tutors, please sign in to answer this question.

1 Answer

The third order Taylor polynomial generated by f(x) at x=0 is of the form
P3(x) = f(0) + f'(0) x + (1/2!) f''(0) x² + (1/3!) f'''(0) x³.
 
With f(0)=0, f'(0)= 1, f"(0)=0, and f'''(0)=2 this becomes
P3(x) =  x + (1/3!) 2 x³ = x + (1/3) x³ .

Comments