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Second Derivative Test - Local Extrema

Second Derivative Test - Local Extrema
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2020-08-05 02:15
FunctionCalculusDerivative
This example demonstrates how to use the second derivative test to determine local extrema of a function. Key mathematical concepts include derivatives and calculus. Using GeoGebra commands such as Tangent, Circle, Intersect, Segment, and Text, the function graph, tangents, and extremum points are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Tangent(A, f) → g
  2. Circle(A, 2) → c
  3. Intersect(c, g) → B, C
  4. Segment(B, C) → h
  5. Text((((("at A (" * a) * ", ") * f(a)) * ")")) → text1
  6. Text(("f'(x) = " * b)) → text2
  7. Text(("f''(x) = " * d)) → text3

AI Drawing Prompt Reference

Draw the graph of a function and its tangent line at point A. Draw a circle centered at A with a radius of 2, and find the intersection points B and C with the tangent line. Connect B and C to form segment h. Display the function value f(a) at point A, and show the expressions for the first derivative f'(x) and the second derivative f''(x) on the graph.
The prompt above was compiled from the original drawing commands and is for reference only.