with inflection points
“Our nations and our world stand at a genuine inflection point in history,” President Biden said during his recent trip to Europe as he addressed a group gathered to talk about a global technology initiative.
Genuine or not, I am tired of inflection points.
For the past couple of years everyone has been talking about inflection points, and I think we need to quit using the term, whatever it means.
What is an inflection point? The website mathworld, one of my favorites, describes it as “a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima.” The site goes on to say, “the first derivative test can sometimes distinguish inflection points from extrema for differentiable functions f(x). The second derivative test is also useful. A necessary condition for x to be an inflection point is f^(”)(x)=0. A sufficient condition requires f^(”)(x+epsilon) and f^(”)(x-epsilon) to have opposite signs in the neighborhood of x .”
I may have missed that in the calculus class I did not take. Continue reading




