Critical point (mathematics)

Common card · No. 358210

In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. More specifically, when dealing with functions of a real variable, a critical point is a point in the domain of the function where the function derivative is equal to zero (also known as a stationary point) or where the function is not differentiable. Similarly, when dealing with complex variables, a critical point is a point in the function's domain where its derivative is equal to zero (or the function is not holomorphic). Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). This sort of definition extends to differentiable maps between ⁠ℝm⁠ and ⁠ℝn,⁠ a critical point being, in this case, a point where the rank of the Jacobian matrix is not maximal. It extends further to differentiable maps...

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