/sci/ - Science & Math

>>12496808
>defining the derivative of a function as its tangent line to the curve at a point
That's a bit of sloppy language and a soon as you make it precise, you'll probably end up with the latter anyway.
Firstly, if you just say "of a function", you're permitting a much to big class of functions (even continuous functions often don't do the job of having a well define tangent line at all points.)
Let's consider polynomials (or maybe certain series, if you can characterize niceness properties succinctly). You say "tangent line" but I don't think you mean the synthetic object or the linear function. Let's say you mean the slope the linear function at a point that coincides with the function in question only once, in the interval where the function is convex or concave.
That slope is already a "rate of change" of the linear function. Although rate of change kinda has a temporal component to it, imho.

Anyway, I'm pretty sure your Prof defines the derivative of a function at a point by the limit, and the dervative of a function in an interval as a function taking you to the pointwise limits.

>>12160288
>Tomasz Kaczynski
lel