We know what you said about the second derivative. So what does this imply for the first one?
Well before $x=2$, the function must be rising! why, because its derivative is positive up to $x=2$ (the 2nd derivative is the first derivative of the first derivative). At $x=2$, it must be stationary. After $x=2$, it must be decreasing as its derivative is negative.
So now this tells that the first derivative has a local maximum at $x=2$, but it doesn't tell us if the maximum is at a positive or a negative (y is greater or lesser than 0). It could be at any arbitrary y value!
So for the actual function,it might not be flat at all at $x=2$ !!! Instead we know for sure that the slope after $x=2$ starts "curling" to the opposite direction from the direction it was curing from, and note, it may have never even become tangential to the x-axis (horizontal)! So if the function's line was the trace of a boat, before $x=2$ it may have been turning left and after $x=2$ it must have started turning right - that's all we can know!
So to your question: clearly the only thing we can deduce from the given information is that there is an inflection at $x=2$
Have a nice day :)