Calculus

Suzanne Doering, Feb 21, 2014


  • 1. The Definition of the Derivative
  • 2. Tangent Line from Secant Lines
  • 3. Derivative Exploration
  • 4. First Derivative as Gradient of Tangent Line
  • 5. The Chain Rule for Derivatives
  • 6. Using cylinders to show how volume of revolution is formed
  • 7. Derivative of Sine Function Exploration
  • 8. Derivative of Cosine Function Exploration

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The Definition of the Derivative

Use this applet to explore how the definition of the derivative relates to the secant and tangent lines at a point (a, f(a)).[br][br]The red slider controls the location of the point (a,f(a)).[br]The blue slider controls the value of "h" that determines the separation of the two points used for the secant line.[br][br]Watch what happens to the secant line as you decrease the value of h. [br]Pay specific attention to the slope in the equation of the secant line shown at the bottom.[br]What happens to the secant line when h = 0? Why?[br][br]Now turn on the tangent line to see how it compares to the secant line.
The Definition of the Derivative
– donalduncan

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