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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
Calculus with 450+ answers. Since you've listed calculus as a topic, I'll assume that your question refers to a real valued function [math]f[/math] defined on an interval [math][a,b].[/math] An example would be to find the maximum and minimum value of the function [math]f(x)=x^3-3x[/math] on the interval [math][0,2].[/math] This is a differentiable function defined on a closed interval, so it takes on its extreme values either at the endpoints, [math]0[/math] or [math]2,[/math] or where its derivative is [math]0.[/math]