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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.
The function f(x) = x2 + 2x + 3 is differentiable everywhere, with the derivative f â²(x) = 2x + 2. This function has a unique critical point â1, because it is the unique number x0 for which 2x0 + 2 = 0. This point is a global minimum of f. The corresponding critical value is f(â1) = 2.