Question

What is the gradient function used for?

Answer 1

The gradient function is a precursor to the fundamental idea of a derivative.

We know that the gradient over an interval can be found by calculating rise/run of any function, but most often in the real world, these functions don't behave in straight lines and so the gradient function is often very wrong.

The idea is to shrink the "run" portion to the smallest size you can think of, and even smaller. That way, you are calculating more and more precise gradients for the function at a certain point. Eventually, calculus provides tools to be able to shrink that interval down to zero, but the gradient function is a good start.