A differentiable function is a type of function that has derivatives at every point within its domain. This means that the slope or rate of change can be determined at any point on the graph.
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The derivative measures how much a function changes as its input changes. It represents the instantaneous rate of change or slope at any given point on the graph.
A line that touches and "hugs" the curve of a differentiable function at only one point, representing the instantaneous rate of change (slope) at that specific point.
A critical point occurs when either the derivative is zero or undefined. These points are important for determining maximums, minimums, and inflection points on graphs.