- Recognize the meaning of the tangent to a curve at a point.
- Calculate the slope of a tangent line using definition, and find the equation of tangent line.
- Calculate the derivative of a given function at a point using derivative definition.
- Chapter 3.1 Defining the Derivative
- p. 228: 1, 3, 11-17 odd, 21-25 odd
- Derivatives-Limit Definition
Exit problems of the session
- Let . Find the slope of the tangent line at and find the equation of the tangent line at .
- Use the definition of derivative at a point to find where .
- The slope of the tangent line to a curve measures the instantaneous rate of change of a curve.
- The equation of tangent line at the point with slope is: .
- We can calculate the slope of the tangent line by finding the limit of the difference quotient with increment
- The derivative of a function at a value is found using the definition for the slope of the tangent line
Videos and Practice Problems of Selected Topics
- Derivative as a concept (7:16) Introduction to the idea of a derivative as instantaneous rate of change or the slope of the tangent line.
- Secant lines and average change of rate (5:16) Consider and find the average rate of change over .
- * Practice: Derivative notation review. (one problem with a guiding text)
- Derivative as slope of a curve (6:09) Estimate the derivative by analyzing the graph of . Then compare the values and by looking at the graph of .
- * Practice: Derivative as slope of curve. (4 problems)
- The derivative and tangent line equations (7:32) The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line.
- * Practice: The derivative and tangent line equations. (4 problems)