Let f be a function that is differentiable on teh open interval (a,b) If f has a relative minimum at (c,f(c)) and a<c<b which of the folowing must be true?
I. f'(c)=0
II. f''(c) must exist
III. If f''(c) exists, then f''(c)>0
a. I
b. II
c. III
d. I and II
e. I and III
okay so i said that the first one has to be true because c must have been a critical point to be a relative minimum so f'(c) must have been equal to zero. I said one is true. But I forgot how f'' relates to the minimum and stuff. at first i thot all of them were true but that is not he case because that is not an answer choice.
I. f'(c)=0
II. f''(c) must exist
III. If f''(c) exists, then f''(c)>0
a. I
b. II
c. III
d. I and II
e. I and III
okay so i said that the first one has to be true because c must have been a critical point to be a relative minimum so f'(c) must have been equal to zero. I said one is true. But I forgot how f'' relates to the minimum and stuff. at first i thot all of them were true but that is not he case because that is not an answer choice.
