Subsection 13.2.5, below, is on “differentiability”. The earlier part of chapter 13 gives a potted, and not error-free, introduction to limits and continuity, and Chapter 12 covers the “first principles” (limit) computation of polynomial derivatives. We’ve included the relevant “worked example”, and the relevant exercises and answers.
The following is just a dumb exercise, and so is probably more of a PoSWW. It seems so lemmingly stupid, however, that it comes around full cycle to be a WitCH. It is an exercise from Maths Quest Mathematical Methods 11. The exercise appears in a pre-calculus, CAS-permitted chapter, Cubic Polynomials. The suggested answers are (a) , and (b) 81/32 km.
The problem, as commenters have indicated below, is that there is no parabola with the indicated turning point and intercepts. Normally, we’d write this off as a funny but meaningless error. But, coming at the very beginning of the introduction to the parabola, it most definitely qualifies as crap.
The following exercise and, um, solution come from Cambridge’s Mathematical Methods 3 & 4 (2019):
Reflecting on the comments below, it was a mistake to characterise this exercise as a PoSWW; the exercise had a point that we had missed. The point was to reinforce the Magrittesque lunacy inherent in Methods, and the exercise has done so admirably. The fact that the suggested tangents to the pictured graphs are not parallel adds a special Methodsy charm.