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- URL: https://x.com/EricLengyel/status/1779680638742000102
- Author: Eric Lengyel (@EricLengyel)
- Posted: 2024-04-15 01:18:23
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1/ @EricLengyel
There’s a neat property about the quadratic formula that most people don’t seem to be aware of. The root given by the plus sign is always where the curve crosses the x axis with a positive derivative, and the root given by the minus sign always has a negative derivative.
2/ @EricLengyel
This is obvious if you plug the roots into df/dx, and it’s true regardless of the sign of a, which determines whether the parabola opens upward or downward. This means you never need to actually calculate the derivative at a root if you want to know which way the curve is going.
Branches: 2024-04-16-davidthomas426-wait-is-completing-the-square-somehow-related-to