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Finding Coordinates Where Gradient is 8

Finding Coordinates Where Gradient is 8
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2015-09-01 20:34
FunctionCoordinate GeometryCalculusDerivativeGeometric Construction
This example demonstrates how to locate points on a function's graph where the gradient is exactly 8, using concepts from coordinate geometry and differential calculus. It involves constructing tangent lines and calculating slopes with GeoGebra commands like LaTeX, Tangent, and Slope, utilizing objects such as f (function), text1-text4, a, P, b, and m. Ideal for high school students learning calculus and analytical geometry.

GeoGebra Commands & Parameters

  1. LaTeX(f, true, true) → text1
  2. Tangent(P, f) → b
  3. Slope(b) → m
  4. LaTeX(m, true, true) → text2
  5. LaTeX(P, true, true) → text4

AI Drawing Prompt Reference

Draw a function curve, mark a point P on it, construct the tangent line at P, display the slope of the tangent, and label both the coordinates of P and the slope value so that the slope equals 8, illustrating how to locate points where the gradient is 8. Include text labels showing the function expression, the tangent slope, and the point coordinates, and ensure the construction order follows the function, point, tangent, slope, and labels.
The prompt above was compiled from the original drawing commands and is for reference only.