Discussion
Three of these four statements about continuity and differentiability hold. The exception is
Answer: B
Differentiability implies continuity but not the reverse. The function \( |x| \) is continuous everywhere yet has no derivative at the origin, where the one-sided slopes are \( -1 \) and \( +1 \). So continuity is the weaker condition, and a corner is exactly the case that separates the two properties
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