This year, I am teaching AP Calc AB for the first time in a while. Thinking about implicit differentiation and I thinkI am going to really emphasize dy/dt notation more than y' as a way to ease the impicit differentiation challenge.

An interesting take on the FTC from a student at our school. Asked for the derivative of the integral of sqrt (t) from 4 to x^2, she identified three cases for the answer. A) 2 < |x| B) 2 = |x| C) |x| < 2 Is she overthinking it, or have I been underthinking FTC?

Trig question : for f(x) = A cos (bx) + C sin (dx) I know that the period is the LCM of the two component periods. Is there a way to find the amplitude? Is amplitude a logical question?

A quick check seems to confirm this. Are these formulas ones any of you have seen before? He could not really explain his insight comfortably. 3/2

His formula seems to check. Someone else then asked about the number of rectangles is the original size was not 8 by 8 but, instead, an m by n rectangle. My student who proposed the original formula thinks this is a sum of sigma 1 to m of (m-x+1) and sigma 1 to n of (n-y+1) 2/2

In Calc BC yesterday I posted a picture of a chessboard and asked for how many squares there would be. We worked our way through to the answer. I then posed the question of how many x by y rectangles there would be. One student proposed (8-x+1)*(8-y+1) 1/2

It has been too long since I checked in on this account and it has been way too long since I blogged about my classes. Hoping to get more engaged again and here is my starting salvo mrdardy.mtbos.org/2025/10/21…

Thinking about this last night watching Knicks and Pacers. Which is a worse situation: Losing game 2 when down 1-0 or losing game 4 when down 2-1? Is this generalizable?

Listening to @DrJYTAA is making me pretty happy right now. Listening here - listen.streamon.fm/wudr

So fun to hear @hpicciotto referenced in the puzzle segment on All Things Considered on @npr this morning. Always fun to run into math friends in the wild world

We looked at the graphs and saw it worked. A question came my way about the Chain Rule here. Since our Taylor was built with derivatives, my Ss expected some implication of the derivative of x^2 to be part of the new expansion. Any smart summary of why not? 2/2

Looking for help in explaining something. Working with Taylor series today. Derived series expansion for y = e^x Showed my Ss that y = e^(x^2) was represented by simply replacing every x in original Taylor with an x^2 1/2