- #1
ElectroPhysics
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Hi
Is it true that derivative of a function is possible only if it is continuous!
Is it true that derivative of a function is possible only if it is continuous!
The condition for a derivative to exist is that the function must be continuous at the point of interest and have a defined slope at that point.
The condition for a derivative is important because it is necessary for the mathematical concept of a derivative to be well-defined and meaningful. Without this condition, the derivative would not have a clear interpretation or purpose.
Yes, a function can have a derivative at only one point if it meets the necessary condition of being continuous and having a defined slope at that point. However, this is not a common occurrence and most functions have a derivative at multiple points.
If a function does not meet the condition for a derivative, then the derivative does not exist at that point. This means that the slope of the function cannot be determined at that specific point.
To check if a function meets the condition for a derivative, you can use the definition of a derivative to see if the limit of the difference quotient exists at the desired point. Additionally, you can visually inspect the graph of the function to see if it is continuous and has a defined slope at the point of interest.