Thread: Taylor Expansion

Rather stuck on the following:

The function f(x) has Taylor expansion a0 + a1x + a2x^2 + ... around x=0.
If a1 = 0, and a2>0 explain why f >= (greater than, OR equal to) a0 near x=0

First of all, am i right in saying this can also be called a Maclaurin series, since we're considering it around x = 0?

And, secondly...well, not really sure where to begin, or how to phrase my answer, I can see why it would be true from the info given..but having difficulty putting it into the correct form...

If anyone can help, it would be greatly appreciated.

Originally Posted by scorpio1

Rather stuck on the following:

The function f(x) has Taylor expansion a0 + a1x + a2x^2 + ... around x=0.
If a1 = 0, and a2>0 explain why f >= (greater than, OR equal to) a0 near x=0

First of all, am i right in saying this can also be called a Maclaurin series, since we're considering it around x = 0?

And, secondly...well, not really sure where to begin, or how to phrase my answer, I can see why it would be true from the info given..but having difficulty putting it into the correct form...

If anyone can help, it would be greatly appreciated.

f'(0)=0, so 0 is a stationary point of f, f''(0)>0 so 0 is a local minima
of f, so for x close enough to 0, f(x)>f(0).

RonL