The process of verifying if a function is differentiable over a certain interval hinges on establishing the existence of the function's derivative for all points within that interval. If the derivative not only exists, but is also continuous throughout the interval, then it can be concluded that the function is differentiable within that interval. Conversely, if these conditions are not met, the function is deemed not differentiable.
| Topic | Problem | Solution |
|---|---|---|
| None | Check if the function \(f(x) = |x|\) is different… | First, we find the derivative of the function. The derivative of \(f(x) = |x|\) is \(f'(x) = x/|x|\… |
| None | Determine whether the following function is conti… | To determine whether the function is continuous at \(a=10\), we need to check three conditions: 1. … |