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Linear Approximation of Quadratic

Audience:

Suppose you want to calculate the function $f\left(x\right)=\left(x-1\right)^{2}$ , however multiplication is very computationally expensive, so you want to approximate it with a linear function near 0<x<1. Looking at the graph of $f\left(x\right)$ , you decide the line should be of the form $l\left(x\right)=a-x$ . Now what?

https://www.desmos.com/notebook/hdp7lm31nw/view

Analytics

3.03 Overall score*

41 Rank

6 Votes

6 Comments

Comments

6.9

simple and well explained

Really nice short introduction to the problem. Alas, it lacks clear motivation. (Multiplication being expensive is probably not something obvious to a general audience). Also, it just ends without any form of conclusion or payoff.

1.4

No clear motivation, no notable exposition (just a bunch of unexplained equations). Desmos was a good choice for interactivity which helps with intuition, but I have no idea what I should be getting an intuition for or why.

3.1

This clever, but I doubt the usefulness. Sure if ² is computationally expensive, then a new formula with the same ² as well as three additional ³ and three more √ would be even worse. Or maybe I am missing something obvious.

2.1

what?

3.6

I liked the setup and the format. Being able to play with a value in desmos was helpful. However, at times, it was confusing what exactly you were doing and why: for example, the part where you took the antiderivative. It left on a cliffhanger, with the question of the total area still being left unanswered.