Mathochism: Smooth derivatives

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Under the compass of Damocles We’ve moved on to derivatives. I’ve been kind of looking forward to them, even if I much prefer the quickie technique over the groan-inducing f(a + h) – f(a)/h one.

Still, the latter choice feels much more comfortable this time. I remember how I agonized over how to apply the formula to functions like √x and x³. I tried getting help from the Calc Dementor, which he gave, albeit begrudgingly and condescendingly.

The Calc Professor’s approach to the painful formula was much better. First of all, she broke everything down very clearly. Then, one of her examples for how to apply it involved √x. It’s like she knew that one would stump students, so she did her best to demystify it.

And I really, really appreciate that!

I’m still struggling with how to identify cusps, corners and vertical lines in a function without seeing the graph, but her explanations in class made a lot more sense than the ones last semester. I liked her colorful way of describing a differentiable point on the function: “It has to be smooth!”

For some reason, I now associate derivatives with the ’80s Sade hit “Smooth Operator.” Is that weird? Or am I just old?

I’m hoping that, between her help and what I remember from last semester, that I can handle such problems on homework better than I did before.

The optimism is still cautious. For now.

All text copyrighted by A.K. Whitney, and cannot be used without permission.


  • I don’t often comment on this series, but I really love it. Watching you progress through the math sequence has been like watching someone meet old friends of mine, and like some of them and hate some of them, but always interesting through different eyes.

    I admire your perserverence through this experiment, and I hope that you continue to explore mathematics, even informally, (and write about it!) when it’s done.

  • Thank you! And if you’re still interested, I would still love to talk to you for the Mathochism book. I’ve put my research on the back burner so I can focus on passing calc, but hope to start interviews again once it’s over.

  • I’d be happy to be interviewed.

    I also thought you might like this. It’s the Weierstrass function, which is continuous everywhere and differentiable nowhere. It’s the unsmoothest function!

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