Question

If the graph of f ′(x) has an x-intercept at x = c, which of the following must be true?
a. The graph of f has a relative minimum or relative maximum at x = c.
b. The graph of f has an inflection point at x = c.
c. The graph of f has an x-intercept at x = c.
d. None of the above is necessarily true.

Answer 1

@mathmate @shiraz14

Answer 2

d

Answer 3

Let's say that \(\Large\rm f'(x)=x~stuff\)
Then f'(x) has x-intercept at x=c if c is a solution to \(\Large\rm 0=x~stuff\).

What does that process remind you of? *cough cough* critical points, yes? 0_o

Answer 4

yes...so since there isnt any mention of critical pts... the answer is d then? @zepdrix

Answer 5

critical points correspond to max/min locations, yes? :)

Answer 6

Oh oh, it says MUST BE TRUE.
Hmmmmmmm

Answer 7

Example:\[\Large\rm y=x^3\]\[\Large\rm y'=3x^2\]\[\Large\rm 0=3x^2\]We can see that y' has an x-intercept at x=0.
So we have a critical point at x=0.But this is clearly neither a max nor a min, ya? :)