Find series given values of derivatives

[boomer22]

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.

 

[morphism]

What you've written down certainly works.

 

[boomer22]

What you've written down certainly works.

thanks a lot

 

[HallsofIvy]

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.

You certainly can check it yourself! If f(x)= 2+ 6x- 4x², what is f(0)? What is f'(0)? What is f''(0)?