Differentiability implies ___________________
continuity
Differentiability implies continuity, but continuity does not necessarily imply differentiability.
In more technical terms, if a function f(x) is differentiable at a point x=a, then it must be continuous at x=a. However, a continuous function may not necessarily be differentiable at all points or any points. The function must satisfy certain conditions, such as having a defined limit as x approaches a, in order to be differentiable.
More Answers:
How And Why Limits Of Math Functions Fail To Exist: Oscillations, Asymptotes, Discontinuity, And Multiple PathsMastering Function Continuity: A Step-By-Step Guide For Math Enthusiasts
Discovering The Power Of Level Curves In Visualization And Analysis Of Mathematical Functions