Higher order derivatives | Chapter 10, Essence of calculus
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when someone asks what the second derivative actually means or how it relates to curvature.
Recommended by 2 people across 2 different months, 2017 to 2020.
What it is
A short 3Blue1Brown video from the Essence of Calculus series that introduces the second derivative, third derivative and higher orders. It uses animated visuals to show the second derivative as the rate of change of the rate of change and as a measure of curvature.
What people said
Recommends Ben Grossmann · 2017-12 · Mathematics Stack Exchange · on “Difference between Slope and Curvature”
I think you would benefit from watching this video [this video] , and from watching the whole series for that matter.
Recommends user808945 · 2020-07 · Mathematics Stack Exchange · on “What is the actual meaning of second derivative?”
You can think of the 2nd derivative as what is the rate of change of the rate of change or how curved does it look. look here for a good info [this video]
Cites joshuaronis · 2020-02 · Mathematics Stack Exchange · on “Second Derivatives to Second Differences”
In these two videos... [this video] [LINK] ...Grant shows how second derivative of $f(x)$ at some point $(x_0)$ are related to the "second differences" of the functoin. Mathematically written: $$[f(x_0 +dx) - f(x_0)]+[f(x_0-dx)-(f(x_0))] \propto \frac{d^2f}{dx^2}(x_0)$$ I'm having a little bit of trouble understanding this...if someone could please explain it, I'd really, really appreciate it. Thank you!