Here's the single most useful trick in all of calculus: the derivative is zero at the top of every hill and the bottom of every valley.

Walk up a hill: you climb (positive slope), the ground levels off at the very top (zero slope), then you descend (negative slope). The instant the slope is exactly zero is the peak.

Same for a valley, upside down: down, flat at the bottom, up.

So to find a function's maximum or minimum, you don't eyeball it — you find where its derivative equals 0.

Why you'll care soon: training any AI model, or fitting any neuroscience model, means finding the settings that make the error as small as possible — the bottom of a valley. The computer finds it by chasing the slope downhill until the derivative hits zero. That's gradient descent, and you just learned its core idea.