Hesse's Rule
Ok kiddo, you know how when you do a math problem that has letters like "x" and "y" in it, you sometimes need to find out how those letters change when you do something else like add or multiply?
Well, Hesse's rule is a way to find out how those letters change when you take the second derivative of the problem - that means you look at how the rate of change, or the slope, of the problem is changing.
Here's how it works: if you have a problem with two letters in it, like x and y, you can write out a thing called a "matrix" that has numbers in it. This matrix tells you how those letters change depending on each other. It's like a secret code that helps you understand how to do the problem better.
But it's important to remember that Hesse's rule only works for certain types of problems - ones that are called "twice differentiable" - which means that you can take the derivative twice and still get a good answer.
So Hesse's rule is basically just a way to find out how things change in a math problem when you're looking at how fast they're changing. It helps people do harder math problems more easily!
Well, Hesse's rule is a way to find out how those letters change when you take the second derivative of the problem - that means you look at how the rate of change, or the slope, of the problem is changing.
Here's how it works: if you have a problem with two letters in it, like x and y, you can write out a thing called a "matrix" that has numbers in it. This matrix tells you how those letters change depending on each other. It's like a secret code that helps you understand how to do the problem better.
But it's important to remember that Hesse's rule only works for certain types of problems - ones that are called "twice differentiable" - which means that you can take the derivative twice and still get a good answer.
So Hesse's rule is basically just a way to find out how things change in a math problem when you're looking at how fast they're changing. It helps people do harder math problems more easily!