Differentiability
Definition
Differentiability refers to the property of a function where it has a derivative at every point in its domain. In other words, the function is smooth and has a well-defined slope at each point.
Analogy
Think of differentiability as driving on a road with no bumps or potholes. When the road is differentiable, you can smoothly navigate through it without any sudden changes in direction or speed.
Related terms
Continuity: Continuity means that a function is unbroken and has no gaps or jumps. It implies that the function can be drawn without lifting your pen from the paper.
Derivatives: Derivatives are measures of how fast a function is changing at any given point. They represent the slope of the tangent line to the graph of a function at that point.
Limits: Limits describe what happens to a function as it approaches a certain value or goes towards infinity. They help determine continuity and differentiability by examining behavior around specific points.
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