I have a question: A tangent, I am told is a line through a specified point (a, f(a)) which touches no other point in atleast one neighbourhood of 'a'. How do I prove from here that a tangent is also a line of best approximation of the function in that neighbourhood? Thanking all in anticipation :) Edit: Another question that comes to my mind is: Why can't there be more than one such lines which suffice to be the "best approximation" of the unique function ? i got this question while reading arturo's pleasant answer.
A tangent, a few doubts
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calculus