Derivatives and Tangent Lines 1

In this introduction to derivatives and tangent lines, the concept of a tangent line to a point on a curve is explored, as well as the slopes of those tangent lines and the derivative. The video uses the slope of the second line to approximate the slope of the tangent lines and introduces the concept of limits. The goal is to understand what it means for a line to be tangent to a curve at a certain point and how to find the slope of the tangent line. The video uses the graph of y = x^2 - 3 as an example and shows how to approximate the slope of the tangent line using the secant line.

An introduction to derivatives and tangent lines to curves.

• What is a derivative?
• What is a tangent line to a point on a continuous smooth curve?
• How do you find the slope of a tangent line to a point on a curve?
• How can you approximate the slope of a tangent line with limits and the slope of secant lines?
• Where can I find an introduction to derivatives?
• How can you estimate a tangent line to a curve at a point and sketch the line?
• When does a tangent line not exist for a curve at a point?
• What is the tangent line and its slope of f(x) = x^2 - 3 at (0, -3)?
• How do you find the slope of the tangent line of f(x) = x^2 - 3 at (1, -2)?
• What is a secant line?
• How do you find the slope of a secant line between two points on a curve?