1. The problem statement, all variables and given/known data I'm trying to determine the number of critical numbers for the function (3x-x^3)^(1/3). 2. Relevant equations Critical numbers are where the derivative of the function is = 0 or does not exist. Critical numbers must also exist within the domain of the function. 3. The attempt at a solution I'm getting five critical numbers. Wolfram Alpha, however, disagrees, saying there are only 2 critical numbers. Who's right? http://www.wolframalpha.com/input/?i=+(3x-x^3)^(1/3)+critical+numbers This is my work: 1/3(3x-x^3)^(-2/3)(3-3x^2) = 0 3 - 3x^2 = 0 x = ±1 If x = 0 that will zero the denominator in the term with the negative root, and f'(x) will subsequently fail to exist. If x = ±√3 that will zero the overall derivative. All these points do exist on f(x).