The discussion revolves around finding the power series expansion of a function \( f[x] \) given specific values of the function and its first two derivatives at \( x=0 \). The subject area pertains to series expansions and calculus.
Some participants express agreement with the proposed series expansion, while others encourage checking the values of the function and its derivatives to validate the solution. The discussion reflects a mix of confirmation and prompting for self-verification.
Participants note the absence of formal equations or methods for verification, relying instead on the provided derivative values and function evaluation at \( x=0 \).
morphism said:What you've written down certainly works.
boomer22 said:Homework Statement
All you know about a function f[x] is:
f[0]=2, f '[0]=6, and f ''[0]=-8.
Write down the expansion of f[x] in powers of x through the x^2 term
Homework Equations
none
The Attempt at a Solution
I think the answer is 2 + 6x - 4x^2 , I just don't have any way to check so I want someone to confirm this.