- #1
rasi
- 18
- 0
i need your helps. thanks for everything.
For a function to be differentiable, it means that the function is smooth and has a well-defined slope at every point. This means that the function has a tangent line at every point on its graph, and the derivative of the function exists at every point.
Differentiability and continuity are related but distinct concepts. A function is continuous if it has no breaks or holes in its graph, while a function is differentiable if it has a well-defined slope at every point. A function can be continuous but not differentiable, and vice versa.
A function is differentiable if its derivative exists at every point. To determine if a function is differentiable, you can use the definition of the derivative to calculate the derivative at a given point. If the derivative exists at that point, then the function is differentiable at that point.
The conditions for differentiability are that the function must be continuous at the point in question, and the limit of the difference quotient (the slope of the secant line) must exist as the distance between two points approaches zero. In other words, the function must be smooth and have a well-defined slope at the point in question.
No, a function cannot be differentiable at a point where it is not continuous. If a function is not continuous at a point, it means that there is a break or hole in its graph, and therefore the function does not have a well-defined slope at that point. A function must be continuous in order to be differentiable.