My question involves the discussion in this thread, which I contributed to back in 2009. https://www.physicsforums.com/threads/point-of-inflection.350149/ My question involves the function f(x) = x^(2n) for n greater than 1. Take f(x) = x^4 for example. You differentiate twice and you get f''(x) = 12x^2. Plug in x= 0 into the second derivative and you get f''(0) = 0. This implies an inflection point at x = 0 as I was taught in my introductory calculus course. However, we all know that f(x) = x^(2n) is a parabola, which does not change concavity, including at x = 0. Is this function an exception to the rule that I was never taught in school? Thanks for any insight you can provide. God I feel so silly for asking this...this topic came up recently and I recalled the comments I made in the above thread...I guess I never really looked into it.