Derivative & Horizontal Tangent Lesson

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Use this GeoGebra Interactive to select a function to see it's derivative and Critical points. [br]Answer the Questions given after the interaction.

Questions

Please use the information from the interaction and answer some of the questions to build your knowledge .

Q1

Define Critical Points/Stationary Points. (see the interaction above : The points on the blue curve)[br][br]Select all the correct options.

The points where tangents (Green lines) are parallel to x-Axis. Random points on the curve. The points corresponding to roots of red curve (derivative of the function) The points like (1,0) , (2,0) and (3,0) etc.

Q2

Facts about the Critical points/Stationary Points (see the interaction above : The points on the blue curve)[br][br]Select all the correct options.

Sometimes True:- Functions have Inflection points. Always true:- Every function will have at least one Critical Point. Never True: There are no tangents on the critical/stationary points. Always True:- All the Critical /stationary points are either maxima or minima for a given function.

Q3

Describe how to work out the Critical /Stationary Points for a given function.

Q4

What are Inflection Points and Describe how to work out the Inflection Points for a given function.

Thank you.

Derivative & Horizontal Tangent Lesson

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Questions

Q1

Q2

Q3

Q4

Information: Derivative & Horizontal Tangent Lesson