Part 4/4:
f'(x) = \lim_{h \to 0} \frac{C - C}{h} = \lim_{h \to 0} \frac{0}{h} = 0.
]
This calculation effectively demonstrates that the derivative of any constant function, regardless of its value—be it 3, 99999, or any other fixed number—is invariably zero.
Conclusion
In summary, the derivative of a constant function is zero, as both intuitively understood through graphical representation and formally proven via mathematical definition. This characteristic underscores a foundational aspect of calculus and will serve as a stepping stone for further exploration of derivatives in varying contexts.
Stay tuned for more discussions in this series that simplify mathematical concepts!