1. ## Linear Algebra

hey I have this question due for an assignment for uni in a couple of days, and I dont really know where to start...

Take a function f that is infinitely differentiable at 0.\
- find a degree 1 polynomial p1(x) = a0 + a1x such that

p1(0) = f(0) and p1'(0) = f'(0)

is this polynomial unique? can you find a degree 1 polynomial so p1''(0) = f''(0)?

where do i start with this one? i just dont get the general way which to start this problem...can anyone help?...i only really want a hint on where to go with it, not the answer as well...im new here so i dont get how it all works

2. ## possible solution

Find a0 and a1 in terms of f(0) and f'(0).

(you aren't studying MATH1220 by any chance are you?)

Hoppo.

3. haha maybe

you wouldnt happen to be adam with longish blonde hair that hangs with sean would you?

4. I don't think so ...

I'm trying to find help with the last bit of that question... what's an infinitely differentiable function? (e^x?)

5. i dont know his last name...sorry i was thinking about the wrong guy

umm infinitely differentiably means you can take infinitely many derivatives of that function... as an example:

y = e^x

is infinitely diff'ble as

y' = e^x
y'' = e^x
...

hope that explains it, im not sure how it works into that part of the question though

6. but you can take infinitely many derivatives of anything can't you? Alot of functions jeventually become zero... but can't you still differentiate them?

7. yeah you can, which is why you do it for the general function f, instead of picking some random function, like you did in a)

ill give you a hint though and say look in your algebra textbook for that question

how do you explain part b)? like any degree one function will have p''(0) = 0 always, so as long as f''(0) = 0 it will work...but how do you explain that the polynomial is unique?