Cauchy Mean Value Theorem

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2015-10-22 03:02

Function Calculus Derivative

This example illustrates the Cauchy Mean Value Theorem, involving derivatives and function graphs. It constructs the graphs of functions f and g, and their tangents on intervals [a, b] and [c, d], demonstrating the theorem's core content. Commands used include Derivative, Intersect, Segment, Roots, Tangent, and Textfield. Suitable for university calculus courses.

GeoGebra Commands & Parameters

Derivative(f) → f'
Intersect(f, c) → A
Intersect(f, d) → B
Segment(A, B) → e
Roots(f'(x) - k, a, b) → C, C_2
Intersect(f, g) → D
Tangent(D, f) → h
Intersect(c, xAxis) → E
Intersect(d, xAxis) → F
Intersect(c, h) → G
Intersect(d, h) → H
Segment(A, E) → i
Segment(B, F) → j
Segment(G, H) → l
Segment(D, C) → m
Textfield(f) → InputBox1