At the top and bottom of a curve (Max and Min), the slope is zero. The “second derivative” shows whether the curve is bending down or up. Here is a real-world example of a minimum problem:
What route from home to work takes the shortest time?
Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.
Subtitles are provided through the generous assistance of Jimmy Ren.