Question:medium
Given below are two statements:
Statement I: A function which is differentiable at a point must also be continuous at that point
Statement II: A function which is continuous at a point is not necessarily differentiable at that point
In light of the above statements, choose the most appropriate answer from the options given below
Given below are two statements:
Statement I: A function which is differentiable at a point must also be continuous at that point
Statement II: A function which is continuous at a point is not necessarily differentiable at that point
In light of the above statements, choose the most appropriate answer from the options given below
Statement I: A function which is differentiable at a point must also be continuous at that point
Statement II: A function which is continuous at a point is not necessarily differentiable at that point
In light of the above statements, choose the most appropriate answer from the options given below
Show Hint
Think of differentiability as a stronger property than continuity.
Differentiability implies continuity, but continuity does not imply differentiability.
Visual metaphor: A continuous path can have sharp corners (like \(|x|\)), but a differentiable path must be completely smooth.
Differentiability implies continuity, but continuity does not imply differentiability.
Visual metaphor: A continuous path can have sharp corners (like \(|x|\)), but a differentiable path must be completely smooth.
Updated On: Aug 3, 2026
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
Show Solution
The Correct Option is A
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