Differentiable
Definition
A function is differentiable if it has a derivative at every point in its domain. This means that you can find the slope of the tangent line at any point on its graph.
Related terms
Derivative: The rate at which a function is changing at a particular point. It represents the slope of the tangent line to the graph of the function at that point.
Continuity: A property of functions where there are no breaks, jumps, or holes in its graph. Differentiability implies continuity, but continuity does not necessarily imply differentiability.
Critical Point: A point on a function where its derivative is either zero or undefined. These points can be local maxima, local minima, or points of inflection.
"Differentiable" appears in:
Study guides (1)
Practice Questions (4)
If a function is differentiable at a point, it must also be:
Which of the following functions is both continuous and differentiable at x = 0?
If a function is differentiable on the interval (a, b), which of the following must be true?
If a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), which of the following statements is true?
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