Calculus inflection point question

[daysrunaway]

Homework Statement

Suppose that f has a continuous second derivative for all x, and that f(0) = 1, f'(0) = 2, and f''(0) = 0. Does f have an inflection point at x = 0?

Homework Equations

none

The Attempt at a Solution

I know that for f'' to have a point of inflection, it needs to change sign near that point, but I can't remember if there's a test for f'' that involves f' to find out if it does. Should I just say that it is impossible to say, since I can't analyze the 'neighborhood' of x = 0 to see if f'' changes sign?

 

[Mark44]

Since f' is continuous for all x, small changes in x correspond to small changes in f'(x). For a value c very close to 0, f'(c) would have to decrease by 2 units in order for it to become negative.

 

[lanedance]

this has some good stuff as well...
http://en.wikipedia.org/wiki/Inflection_point

also, how about considering the function
$$f(x) = 1+2x$$