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Which way does the implication run?

Exercise and reference answers

Items
  1. Item
    Differentiable, therefore continuous
    Category
    Always follows
  2. Item
    Differentiable at a point, so continuous there
    Category
    Always follows
  3. Item
    Continuous, therefore differentiable
    Category
    Does not follow
  4. Item
    Continuous at a point, so differentiable there
    Category
    Does not follow
Categories
  1. Item
    Always follows
  2. Item
    Does not follow

Explanation

Differentiable implies continuous, never the reverse. Source: syllabus Maths, Ch 5 Continuity and Differentiability.
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