Answer
See the explanation
Work Step by Step
For a function to be differentiable on an open interval, it means that the function has a derivative at every point within that interval, except possibly at the endpoints of the interval. In other words, the function is smooth and continuous, and its rate of change is well-defined at every point within the interval, allowing us to calculate the slope of the tangent line at any interior point.
On the other hand, for a function to be differentiable on a closed interval, it means that the function is differentiable at every point within the interval, including the endpoints. This implies not only that the function is smooth and continuous within the interval but also that its derivative exists at every point, including the boundary points.
In summary, differentiability on an open interval requires smoothness and continuity within the interval except possibly at the endpoints, while differentiability on a closed interval extends this requirement to include the endpoints as well.
