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. Jan 26 | Sun from Los Angeles, CA | 1 Answer | 0 Votes Mark favorite Subscribe Comment
The third order Taylor polynomial generated by f(x) at x=0 is of the form P_{3}(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 P_{3}(x) = x + (1/3!) 2 x³ = x + (1/3) x³ . Jan 26 | Andre W. Comment Comments Thanks a lot. Jan 26 | Sun from Los Angeles, CA Comment
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