Having covered derivatives, optimization principles, and gradients, we now connect these concepts to a practical machine learning scenario. This chapter demonstrates how calculus facilitates the process of model training through optimization.

Here, you will learn to:

• Apply the concept of a cost function to a simple linear model.
• Calculate the gradient of the cost function with respect to the model's parameters.
• Observe how these gradients are used in a gradient descent step to update parameters.
• Understand the function of the learning rate in this process.

We will work through an example using simple linear regression ($y = mx + b$). You will see how calculating the partial derivatives of a cost function allows us to systematically adjust $m$ and $b$ to minimize error, illustrating the core mechanism behind training many machine learning models.