Hey guys , i am currently in lecture 10. I totally understand where the linear approximation comes from. But i don;t quite get how we derived the quadratic approximation. Has the professor explained it already or did he just state it with a plan of explaining where it comes from later. I assume it has something to do with Taylor expansion?
OCW Scholar - Single Variable Calculus
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There's a good explanation in the end of lecture 9 when he does a quadratic approximation of a quadratic equation, and proves (as expected) that the best quadratic approximation of a quadratic equation is itself.
Using the lecture clips from the Scholar 2010 course is sometimes confusing - I'm following the lectures from the 2006 and checking with the 2010 website.
Yes, you are right. You can see the quadratic approximation as Taylor expansion but without terms whoose order higher than 2.