Derivative Graphing Example by Laura Kinnel (3)
Loading the math board and drawing, please wait…
In collections
Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function. The key mathematical concepts involve the geometric meaning of derivatives and their construction. The GeoGebra commands used include f', a, A, g, B, h, b. It is suitable for high school or university mathematics courses to help students understand the relationship between a function and its derivative.
GeoGebra Commands & Parameters
f(x) = 1 + 1 / xf'(x) = f'(x)Numeric a(-7)(a, f(a))g(x) = If[a - 1 ≤ x ≤ a + 1, f(a) + (f'(a) * (x - a))](a, f'(a))f'(x)Boolean b(false)
AI Drawing Prompt Reference
Draw the graph of the function f(x) = 1 + 1/x and its derivative. First, draw the graph of the function. Then, draw a point A on the x-axis with an x-coordinate of -7. Next, draw the tangent line g at point A, with its x-axis range from 1 unit left to 1 unit right of A. Finally, draw the value of the derivative at point A.
The prompt above was compiled from the original drawing commands and is for reference only.