Question

the function x^x has critical point at x=​

Answer 1

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Definition of a critical point: a critical point on f(x) occurs at x0 if and only if either f '(x0) is zero or the derivative doesn't exist. Definition of a local maxima: A function f(x) has a local maximum at x0 if and only if there exists some interval I containing x0 such that f(x0) >= f(x) for all x in I.