SUMMARY
The function │x^2-4│ is not differentiable at x = -2 and x = 2. This conclusion is reached by analyzing the limits of the derivative from both sides at these points. The definition of the derivative, which involves limits, reveals that the left-hand limit and right-hand limit differ at these critical points, confirming non-differentiability.
PREREQUISITES
- Understanding of the definition of the derivative
- Knowledge of limits in calculus
- Familiarity with piecewise functions
- Basic algebraic manipulation skills
NEXT STEPS
- Study the concept of piecewise functions in calculus
- Learn about limits and continuity in more depth
- Explore the implications of non-differentiability in real analysis
- Practice finding derivatives of absolute value functions
USEFUL FOR
Students of calculus, mathematics educators, and anyone interested in understanding the differentiability of piecewise functions.