List of top Mathematics Questions on Continuity and differentiability asked in UP Board XII

Prove that every differentiable function is continuous. Examine continuity and differentiability of the function \[ f(x) = |x + 2| \text{at} x = -2. \]
Prove that \( f(x) = |x - 2| \) is not differentiable at \( x = 2 \).