In mathematics, a function is said to be "differentiable" at a point if it has a defined derivative at that point. This means that the function has a well-defined slope, which represents how the function changes as its input changes. A differentiable function is smooth and continuous, without any sharp corners or breaks. For a function to be differentiable over an interval, it must be differentiable at every point within that interval. Common examples of differentiable functions include polynomials, exponential functions, and trigonometric functions. However, functions like the absolute value function have points where they are not differentiable due to sharp turns.