Derivative of an Inverse Function

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2017-02-26 07:37

Function Calculus Derivative

This example demonstrates the derivative of an inverse function. Key mathematical concepts include derivatives and inverse functions. Using GeoGebra commands such as Mirror, Tangent, and Slope, the inverse function's graph is constructed, and the changes in its derivative are observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Mirror(f, g) → f_1
Textfield(f) → InputBox1
Mirror(h, g) → h_1
Textfield(a) → InputBox2
Textfield(b) → InputBox3
Mirror(f, g) → f_2
Point(f) → A
Tangent(A, f) → i
Slope(i) → m
Circle(A, 2) → k
Intersect(k, i, 1) → B
Intersect(k, i, 2) → C
Vector(A, C) → u
Vector(A, B) → v
Intersect(j, f_2) → D, E
Tangent(D, f_2) → l
Circle(D, 2) → p
Intersect(p, l, 2) → F
Intersect(p, l, 1) → G
Vector(D, F) → w
Vector(D, G) → n
Slope(l) → m_1