Second Derivatives and Beyond
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Let’s be honest: not much has changed since kindergarten. We still get to draw lines and pictures in calculus class. Hard to believe your tuition goes to help teaching you how to draw lines.
We said inflection, not infection. This is an upbeat take on first derivatives, second derivatives, and points of inflection. You could call it calculus with a smile.
Critical points aren’t something to fear. There isn’t a mutant cat lurking behind them. Just in case, learn how to spot those critical points before the creepy cats spot you.
The first and second derivative tests sound like something your doctor would do to check if you’ve contracted the ebola virus. You have nothing to worry about. This link shows you how an engineer is more likely to need this test than a doctor.
How do you know if you are at a global extremum like the peak of Mount Everest or the bottom of the Marianas Trench? What if you’re at a local extremum like Mount Kilimanjaro or at the bottom of Lake Erie?
Most people try to avoid their relatives. Imagine actively trying to find them instead. Relative extrema, that is.
When your art teacher tried to teach you how to draw a rabbit, it might have felt like pulling a rabbit out of a hat. Drawing functions are easier, especially once you know their derivatives.
You need to be at one with polynomial functions. This video about extrema of polynomials will put you in a zen-like state.
Knowing calculus helps you build bridges. At least it helps these guys. Check out this video of how a bridge is made by finding a minimum of a structural function.
Games and Tools
Anything you can do with complicated computer code, you can do with a computer spreadsheet. It’ll just take you a while to make it look this good. Here’s a numerical first and second derivative plotter for Excel.