Amazing work i really was confused about this because my textbook(stewarts early transcendentals) adds a strange condition for this test which is that the second derivative needs to be continuous near c (i think it is enough for it to be continuous at c) and i can not see why that is necessary.
@@wowfmomf6126 Sorry, late answer, but no need to suppose any continuity of f'' anywhere. In terms of the second derivative, it is actually enough that f''(c) exists and is positive or negative. Here, I assume that f'' exists on (a,b) but outside of f''(c) existing, I actually just need to know that f' exists on (a,b). So, here, I am actually assuming more than I need.
Amazing work i really was confused about this because my textbook(stewarts early transcendentals) adds a strange condition for this test which is that the second derivative needs to be continuous near c (i think it is enough for it to be continuous at c) and i can not see why that is necessary.
Btw subscribed this an underated channel.
@@wowfmomf6126 Sorry, late answer, but no need to suppose any continuity of f'' anywhere. In terms of the second derivative, it is actually enough that f''(c) exists and is positive or negative. Here, I assume that f'' exists on (a,b) but outside of f''(c) existing, I actually just need to know that f' exists on (a,b). So, here, I am actually assuming more than I need.
lovely proof :)
Very nice name of the university