critical points

1. In math, critical points of a function are the points of a function where the derivative is 0 or undefined. In other words, they are the places where the function is horizontal, or there are points or gaps where there is no tangent line. Often times these points are turning points: they are where a function changes from increasing to decreasing, or vice versa. Not always, but often. In calculus, these points are called “critical” because they offer us a roadmap of the function and it’s behavior. They give us a nice summary of what is going on. And they also include points of interest such as maximums or minimums.

2. The word “critical”, outside of math, has a few meanings:

  • 2a. Very important, crucial
  • 2b. To point out the flaws, to critique
  • 2c. Something that offers analysis of a work
  • 2d. Having the potential to become disastrous (ie critical condition)

So this blog, this collection of thoughts, plays on both of these definitions. These are thoughts that are critiques and analysis, of things that are important to me. They are writings about my personal turning points to give you a roadmap of my mind, where I have been, and where I am now.

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