I have been teaching this subject for a very very long time.  As a Teaching Assistant in all  the schools I was a graduate student, that’s NUS, York U and Univ of Rochester.  Even as an undergraduate, I teach students who are preparing for ‘A’ Math.  There are jingles I love to repeat, like “Lo Dee Hi Minus Hi Dee Lo over Lo Lo”, history I love to tell about Sir Issac Newton and other people like Leibnitz and Archimedes.  Other side subject like the confusion on whether Newton was born in 1642 or 1643, and other humour that I found on line and even made some up myself.

But there are a few things I don’t know.  For instant, I don’t recall learning SOHCAHTOA of trigonometry, although maybe a somebody from Thailand in NUS may have mentioned it.  And the names and uses in the third derivatives.

##### The first derivative measures the slope of the tangent at a point. The second derivative measures the concavity (at a point). And the new thing I learn is that the third derivative measures the osculating parabola of the curve at the point.  More of that is on a forum by Steven Schot.  See GIF below:

Osculating Parabola

Here is something funnier: If s=f(t) is the displacement function (thing of it as distance), its first derivative is called the instantaneous velocity; its second derivative is known as the acceleration, and its third derivative starts with a “j”.  It is called the JERK.  Then I asked my class, what do you get if you take the 3rd derivative of a pound of beef? Half the class got the answer and laughed.