Mean Value Theorem Graphical Introduction
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Average Value
This applet visually introduces the Mean Value Theorem, a fundamental theorem in calculus that states that for a continuous function on a closed interval, there exists at least one point where the derivative equals the average rate of change over the interval. By constructing functions, lines, and intersection points, it illustrates the core idea of the theorem. Suitable for high school math teachers and students to understand basic calculus concepts.
GeoGebra Commands & Parameters
Function((-x^(2)) + (5 * x), x1, x2) → pFunction(p, -30, x1) → fFunction(p, x2, 30) → gLine(A, B) → bIntersect(Derivative[p], (p(x2) - p(x1)) / (x2 - x1)) → CFunction(f, -2, 7) → hLine(E, F) → e