The best possible outcome.
Using derivatives to find the maximum or minimum values of a function.
Fermat developed early methods for maxima and minima before Newton fully formalized calculus.
The peak of the mountain has a slope of zero.
Plain English: If you throw a ball in the air, at the very highest point, it stops moving up for a split second before falling down. Its speed (derivative) is zero. We use this to find the best price, max profit, or min cost.
Real-world example: Packaging Design. Calculating the dimensions of a soda can that holds the most liquid but uses the least amount of aluminum (minimizing surface area).
Forgetting to check the endpoints. Sometimes the best answer is at the very beginning or very end, not at the peak in the middle.