Tangent Lines with No Calculus: Thank You Descartes et al скачать в хорошем качестве

Tangent Lines with No Calculus: Thank You Descartes et al

Here's a curious fact: Divide a polynomial expression p(x) by the quadratic (x-a)^2 and get a linear remainder mx+b. Then the line y=mx+b is precisely the tangent line to the graph of y = p(x) at x = a. WHOA! This follows some work of Fermat and Descartes before the invention of calculus. Contemporaries even proved the First Fundamental Theorem of Calculus without calculus. DOUBLE WHOA! This deep dive into math goes into it all. Enjoy! 00:00 Tangent Lines 03:18 Dividing Polynomials and the Astounding Claim 09:18 An Example of Descartes' Approach 14:13 Descartes' General Insight 19:32 Unusual Tangent Lines 21:45 A Practice Example 26:06 Explaining the Opening Claim 29:10 The First Fundamental Theorem of Calculus 33:34 References