The discussion revolves around understanding the Mean Value Theorem (MVT) without relying on geometric visualization, focusing instead on numerical reasoning and real-world applications. Participants explore how to intuitively grasp the theorem's implications through various examples and analogies.
Participants express varying degrees of clarity and understanding regarding the MVT without geometric context. There is no consensus on a singular approach or example that effectively conveys the theorem numerically.
Some participants note that the original question may be too vague, indicating potential limitations in the clarity of the inquiry. The discussion also touches on assumptions about continuity and the nature of derivatives.
What do you want to know? A real world problem which can be solved due to the main value theorem? What should numerically mean? Numerically we always only get an approximation, as the likely mean value isn't rational.archaic said:Hello guys, is it possible to "see" the mean value theorem when one is only thinking of numerical values without visualizing a graph? Perhaps through a real world problem?
By numerically I meant reasoning without resorting to geometry. In other words, how can one foster an intuition for this without seeing a graph?fresh_42 said:What do you want to know? A real world problem which can be solved due to the main value theorem? What should numerically mean? Numerically we always only get an approximation, as the likely mean value isn't rational.