MathPlotAI Logo MathPlotAI

Function Derivative and Gradient Function

Function Derivative and Gradient Function
Loading the math board and drawing, please wait…
2014-01-12 14:57
VectorFunctionCalculusDerivative
This example visually demonstrates the derivative of a function as its gradient function, both graphically and through calculation, covering core concepts in calculus. It utilizes GeoGebra commands like Textfield, Simplify, Vector, EvaluateDerivativePolynomial3, Tangent, and Slope. Ideal for high school and above learning basic calculus principles.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Simplify(f'(x)) → f'
  3. Vector(P, P') → u
  4. EvaluateDerivativePolynomial3(n, f') → text4
  5. Vector(P', P_y) → v
  6. Tangent(P, f) → a
  7. Slope(a) → m

AI Drawing Prompt Reference

Draw a function graph and show its derivative as a gradient function. Mark a point on the function graph, draw a vector from this point to the derivative curve to represent the direction of the derivative. Also, draw the tangent line at this point and label its slope. Display the derivative expression and the slope value next to the graph as text to illustrate the relationship between the derivative and the gradient function.
The prompt above was compiled from the original drawing commands and is for reference only.