@jimh
Jim H
commented
@Andrea S. I find it interesting how varied the terminology can be. In the U.S. we consider #(0,0)# a point of inflection for #f(x) = x^(1/3)# because the concavity changes at that point. But, of course #f''(0)# does not exist. Here the necessary conditions for #(a,f(a))# to be an inflection point are #a# is in domain of #f# and #f'(a) = 0# or #f'(a)# does not exist. (The additional requirement is that the concavity changes at #(a,f(a))#.)
on
What are the points of inflection, if any, of #f(x) = x^4/12 - 2x^2 + 15 #?
@jimh
Jim H
commented
@Steve Thank you! I've learned new terminology. In the U.S. a point of inflection is a point on the graph of #f# at which the concavity changes. So we do not count #(0,0)# as an inflection point of #f(x) = x^4# although we would for #f(x)=x^5#. If I've understood your explanation, you would call both of those stationary points of inflection?
on
What are the points of inflection, if any, of #f(x) = x^4/12 - 2x^2 + 15 #?