Difference between Continuity and Differentiability in Engineering Mathematics

Continuity in engineering mathematics refers to the smoothness of a function's graph, indicating that there are no sudden jumps, holes, or disruptions in its behavior over its entire domain. Differentiability, on the other hand, implies that a function has a well-defined derivative at a given point, signifying how the function's output changes concerning its input. A function can be continuous but not differentiable at a point if it has a sharp turn or a cusp at that point, and it can be differentiable but not continuous if there's a discontinuity or a jump in its graph.