The Four Horsemen Of Non-Differentiable Functions

Behold! The mathematical apocalypse has arrived! These four graph shapes strike terror into the hearts of calculus students everywhere. Each one represents a point where derivatives throw up their hands and say "I quit!" The sharp corner, the vertical line, the cusp, and that chaotic mess in the bottom right (which looks like my brain after finals week) are all places where differentiation becomes mathematically impossible. Calculus professors use these as torture devices, cackling maniacally while students desperately try to find slopes where none exist. These aren't just curves—they're the villains in every calculus nightmare! Next time someone says math is smooth and predictable, show them these mathematical rebellions!