Derivative visual meaning

Question

Edit: I figured out on my own but here is question:

Question: Find the visual meaning of the numerator of: $\lim\limits_{h \to 0} \frac{f(x+h)-2f(x)+f(x-h)}{h^2}$

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So, I found this:

Is this how the graph looks like?

Answer 1

It is closely related to the length of the vertical segment from $(x,f(x))$ to $(x,L(x))$ where $L$ is the secant line between $(x-h,f(x-h))$ and $(x+h,f(x+h))$. This like the second derivative is a measure of deviation from linearity near $x$.