Slope of a Function at a Point with Calculus

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Slope of a Function at a Point

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  1. The Math Sorcerer
  2. slope
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  4. calculus
  5. point
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I'm trying to get ready for theroy, proofs, and definitions, where would I go to find out how to prove the derivative is the slope.
Like I know that to be assumedly true, but I've never proved it myself.
So I think I need to start with the definition of what a derivative is and go from there. Right down the assumption, what the definition provides, and the end point, then try to explain the interim pieces with logic.
(I've never taken any proof/theory courses, only exposure from an uppergrad professor I got to sit-in with, but never recorded lecture, notes, definitions, proofs, theory. -- I more of just wanted to soak it all in and be exposed to what comes next, I just find maths awesome like that even if I don't have any idea what's going on.)
Unrelated note for myself, *need to check out (chain or product rules), and see why factorials are naturally eliminated, seemed interesting from something I watched earlier :)

tauceti