Having explored derivatives as measures of instantaneous change, we now turn to a key application: using them to find optimal points in functions. This process, known as optimization, is central to how many machine learning models learn from data.

In this chapter, you will learn how derivatives are used to locate the minimum or maximum values of a function, often by finding where the derivative equals zero ($f'(x) = 0$). We will examine the concept of cost functions (or loss functions) in machine learning, which measure how well a model performs, and understand why minimizing these functions is the objective. You'll be introduced to gradient descent, a fundamental algorithm used to iteratively minimize cost functions. We will explain how the derivative provides the direction needed for gradient descent and visualize this process to build intuition.