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Sketch the Derivative of Function f

Sketch the Derivative of Function f
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2020-09-21 06:03
FunctionCalculusDerivative
In collections Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function f based on its graph. Key mathematical concepts include derivatives and function graphs. GeoGebra commands such as f, f', a, A, g, B, h, b are used to construct the graph. Suitable for high school calculus education and learning derivative concepts.

GeoGebra Commands & Parameters

  1. f(x) = (2 * sqrt(x + 4)) - 3
  2. f'(x) = f'(x)
  3. Numeric a(-7)
  4. (a, f(a))
  5. g(x) = If[a - 1 ≤ x ≤ a + 1, f(a) + (f'(a) * (x - a))]
  6. (a, f'(a))
  7. f'(x)
  8. Boolean b(false)

AI Drawing Prompt Reference

Draw the graph of function f defined as (2 * sqrt(x + 4)) - 3 and its derivative f'. Mark the point P at x = -7, and draw the tangent line g passing through P that closely touches the f graph nearby. Also, plot the derivative f' and show the slope of the tangent line.
The prompt above was compiled from the original drawing commands and is for reference only.