1. The problem statement, all variables and given/known data The inflection points are where the function changes its concavity, and can be found through the second derivative of the function... so, I have been given this equation: f(x) = x^4 - 2x^2 - 1 and I have to find the inflection points. 2. Relevant equations 3. The attempt at a solution I derived it twice to get the second derivative: f`(x) = 4x^3 - 4x f``(x) = 12x^2 - 4 which can be written as: 4(3x^2 - 1) I ran a quadratic equation and got x = +- (sqrt(3) / 6) So my question is, are these the inflection points, since the function is continuous on those point... Is the difference between Inflection points and critical points that the critical points tell you where the slope reaches 0 if there is continuity at that point, and that they allow you to find whether the function is increasing or decreasing in those intervals, and the inflection points just tell you where exactly the function switches concavity? What more can inflection points do for you?