This lecture covers examples of using derivatives, such as calculating the equation of the tangent line to the graph of f(x) = (π - x)² sin²(x) at the point of abscissa xo = 1/12. It also explores finding points on the graph where the tangent line has a specific equation. The instructor demonstrates how to determine the abscissa xo for the tangent line to pass through a given point. Through various mathematical calculations and equations, the lecture illustrates the application of derivatives in solving real-world problems.