Given a list of N integers, how to find out if the second derivative is positive or negative? Let's say I have a list where N=10, such as [45,34,56,22,33,44,34,34,43,35].
I would like to know if the second derivative is positive or negative, in other words, if the rate of change of these numbers is itself increasing or decreasing.
I took calculus in college 20 years ago. I would know how to do that if I had a function but I don't remember how that can be accomplished with just samples.
Can someone explain me the rationale behind the process?

I will probably plot the points on an x-y axis, find a polynomial (or exponential regression) and take the second derivative of the function that approximate the data. Alternative:you could use numerical differentiation, but you will need to take more points.
you need to evaluate:
$$ f'(x) \approx \dfrac{f(x+h)-f(x)}{h} $$
for $h$ very small (if you are doing engineering or physics calculations $ h \approx 10^-3$ 
or much smaller.
