Find the slope of ##y=x^2+4## at (-2,8) and the equation for this line.
The Attempt at a Solution
This problem is intended to give an intuition on how limits work and I think I get the general idea.
If we want to find the rate of change (or slope) of some point on a function f(x), we essentially "close in" on that point, a, with another point until they're virtually the same point. This creates a tangent line to the point on the graph of the function and we can take the slope of that line and thus know the rate of change of f(x) at that point, a. There are other specifics, but I'm just looking for an answer as to what is happening on this worksheet (attached).
I understand everything up to the point until we set h=0. If we want to close in on the point (-2,8), wouldn't we want to approach that x-value? And since we haven't seen how to take a limit yet, set h equal to -2 rather than 0?