A differentiable function is a function whose derivative exists at each point in its domain. This means the function is both continuous and smooth, with no sharp corners or cusps.
Continuous Function: A function that does not have any abrupt changes in value; it can be drawn without lifting your pen from the paper.
Derivative: A measure of how a function changes as its input changes; formally, it represents the slope of the tangent line to the graph of the function.
$\lim$ (Limit): $\lim_{x \to c} f(x)$ describes the behavior of $f(x)$ as $x$ approaches some value $c$. Limits are foundational for defining derivatives and continuity.