Chapter 4 of 10All chapters
Chapter 4 of 10
Finding the best value
Where the slope is zero.
Peaks and troughs
At a maximum or minimum the curve is momentarily flat, so its derivative is zero. Solving for that condition is how optimisation problems are set up.
- The second derivative says which one it is: negative for a peak, positive for a trough.
- Check the endpoints too; the best value is sometimes at a boundary.
Everywhere in practice
Least material for a given volume, cheapest route, best price, lowest error. Every one of them is a search for a point where the slope vanishes.