Part 5/5:
For values greater than zero, the derivative is ( f'(x) = 1 ).
For values less than zero, the derivative is ( f'(x) = -1 ).
However, at ( x = 0 ), the limits from the left and right do not agree, hence the function is not differentiable at this point.
Conclusion
In summary, the concepts of differentiability, the different notations used in calculus, and the method of graphing derivatives are crucial in understanding how functions behave. Knowing the types of situations where a function becomes non-differentiable helps learners identify potential problems in calculus and further reinforces mathematical concepts.
With this understanding, one can tackle differential calculus with a clearer perspective. Stay curious and keep exploring the mathematical world!