Differentiable refers to a property of a function in calculus. A function is considered differentiable if its derivative exists at each point in its entire domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. This means that the function is smooth and does not contain any breaks, angles, or cusps. Additionally, a differentiable function is always continuous, but not all continuous functions are differentiable. The derivative of a function is a key concept in calculus and provides information about the rate of change of the function at various points. Differentiability is determined using limits and continuity, and a function is differentiable everywhere its derivative is defined.
In summary, a differentiable function is one for which the derivative exists at every point in its domain, and it is a fundamental concept in calculus for understanding the behavior of functions and their rates of change.
