Differentiability and Horizontal and Vertical Tangent Lines

Use slope to find the location of horizontal and vertical tangent lines. Using the derivative of a radical function, the presenter finds the points where the derivative is zero or undefined on a given interval. The 26th in a series of 31 videos shows graphically the location of the horizontal and vertical tangent lines to the function. The resource goes on to interpret the vertical tangent lines in terms of the differentiability of the function.

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Instructional Ideas
  • Have pupils visually estimate the point on the graph where the tangent line would be horizontal or vertical
Classroom Considerations
  • The class should be able to find the values in which a function is not defined
  • Individuals need to be comfortable using the product rule and chain rule
  • This resource is only available on an unencrypted HTTP website. It should be fine for general use, but don’t use it to share any personally identifiable information
Pros
  • Shows all the steps involved in the simplification of the expression
  • Explains and justifies the algebraic manipulations
Cons
  • None