If we know f(3)=2.1, f'(3)=-3.6,f"(3)=5.4 and |f'''(z)|

Question

If we know f(3)=2.1, f'(3)=-3.6,f"(3)=5.4 and |f'''(z)|<9.2 for z between 3 and 3.012. What is the best esitmate of f(3.012) and what is the error bound"?" ;

anonymous · Answer

Sounds like taylor series$$f(x)=\frac{f(a)}{0!}(x-a)^0+\frac{f'(a)}{1!}(x-a)^1+\frac{f''(a)}{2!}(x-a)^2...$$ With a=3

anonymous · Answer

I'm not sure how |f'''(z)|<9.2 would help with that, though.

anonymous · Answer

Then just insert x=3.012 for the approximation.

anonymous · Answer

expansion is  maybe 
$$2.1-3.6(x-3)+2.7(x-3)^2+\frac{f'''(3)}{6}(x-3)^3+...$$

anonymous · Answer

last term gives the bound for the error if i am not mistaken.

anonymous · Answer

$$\frac{9.2}{6}(.012)^3$$ would be the error i think

anonymous · Answer

are any of you familiar with maple? i need some help checking some work i did