Decide the MacLaurin polynom

[Pirate]

Decide the MacLaurin polynom of the 3rd order to:



I tried beginning by deciding the derivate f'(x) and I got f'(x) = 2x*cos(x^4). But does that even help? I guess I need to know the original function f(x) to decide the MacLaurin polynom?


Can you please help me with this?

 

[DrPhil]

Decide the MacLaurin polynom of the 3rd order to:

View attachment 2660

I tried beginning by deciding the derivate f'(x) and I got f'(x) = 2x*cos(x^4). But does that even help? I guess I need to know the original function f(x) to decide the MacLaurin polynom?


Can you please help me with this?

Yes, that is the way to start - and well done. The next thing to do is evaluate f(0) and also f'(0). Is it a surprise that f'(0)=0? Look at the symmetry of the function f(x). Can you convince yourself that it is an even function? What does that symmetry tell you about odd derivatives?

Find f''(x) by differentiation, and then evaluate f''(0).

How much farther do you need to go?

 

[Pirate]

Alright, I understand now, thanks.

I hope I can get help with some more calculus questions in this forum because I think I will have many...