Method of steepest descent

Imagine you are trying to get down from a big mountain, but you don't know the easiest way to get to the bottom. You have a map, but it's not very detailed, and you don't want to walk around aimlessly. So, you decide to use the method of steepest descent.

Here's how it works: you start by looking around and finding the direction that is the steepest downhill. This means looking for the direction where the slope of the mountain is the highest. Once you find it, you start walking in that direction until you reach a point where the slope decreases. Then, you stop and look around again for the new direction that is the steepest downhill, and repeat the same process.

By using this method, you gradually move downhill in the fastest possible way. You don't waste time walking up and down unnecessary slopes, and you don't get lost. This method can be used in many different situations, such as finding the fastest way to solve a complicated math problem or finding the quickest way to get from one point to another in a city.

So, the method of steepest descent is like finding the quickest way downhill on a mountain or any situation where you want to optimize something by choosing the direction that gives you the best rate of change.