Ostrowski Inequality Visualization: Error Bound via Derivative and Midpoint

This GeoGebra example dynamically illustrates Ostrowski's inequality: for a differentiable function f on [a,b], the difference between the integral average and the function value at a point is bounded by the maximum absolute derivative times the interval length. The core mathematical concepts include integral mean value theorem refinements, derivatives, maxima, arithmetic and geometric means. Construction details: the Derivative command computes f', the Max command finds the maximum of |f'|, Segment constructs the interval, Textfield and InputBox allow parameter input, and dynamic text displays both sides of the inequality for comparison. Suitable for university-level mathematical analysis or numerical analysis courses, this tool helps students intuitively grasp how the error bound depends on interval length and derivative supremum, and serves as a visual aid for proving related inequalities.