Homework Help Overview
The discussion revolves around finding a function defined on the interval [-1,1] that is continuous, differentiable on (-1,1), but has a derivative that is not differentiable on that same interval. This relates to properties of the Fundamental Theorem of Calculus.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the relationship between the Mean Value Theorem and the properties of the function in question. There are attempts to connect the requirements of the problem with the Fundamental Theorem of Calculus. Some suggest starting with a nondifferentiable function and integrating it to find the desired function.
Discussion Status
Participants are actively discussing potential functions that meet the criteria, with some suggesting the absolute value function as a candidate. There is acknowledgment of the need for a function that is once differentiable but not twice differentiable, indicating a productive exploration of ideas.
Contextual Notes
There is a focus on the properties of differentiability and continuity, with specific attention to the behavior of the function at the point x=0. Participants are navigating the constraints of the problem without reaching a consensus on a specific solution.