No, a function cannot be differentiable without being continuous. Differentiability implies continuity. If a function is differentiable at a point, it must also be continuous at that point. This is because finding a derivative involves calculating a limit, and for that limit to exist, the function must not break or jump at that point. However, the reverse is not always true, a function can be continuous but not differentiable, such as the absolute value function at x=0, which is continuous but has a sharp corner, making it non-differentiable at that poin