Question

Which of the following are true?
f (x) has no concavity when f ‘(x) = 0.
f (x) has no concavity when f (x) = 0.
f (x) has no concavity when f ‘’(x) = 0.
f (x) has no concavity when f ‘(x) = 0 and f ‘’(x) > 0.

Answer 1

Suggestion: re-write everything to read, "f(x) HAS (what kind of?) concavity when ... ", and review what concavity is and how we determine it.

Answer 2

question makes no sense. All of them are sometimes true and sometimes false

Answer 3

The only time for a continuous function to have no concavity is when it is a constant function

Answer 4

@sourwing : there's more to it than that.
For example: Let's look at the first statement: "f(x) has no concavity when f'(x)=0."
That's false. Why? If f'(x)=0, there's the possibility that there's either a minimum or a max at that x value, OR a horizontal point of inflection. If there's a minimum, the graph will be concave UP, and if there's a max, the graph will be concave DOWN. So in either of these two cases, the given statement is false.

Answer 5

okay,

Answer 6

@mathmale, it's asking for which statement is TRUE, so you're, the first case isn't true.

Answer 7

How does that statement of yous add to the discussion? I concluded that the first statement is false, which means that we'll eliminate that statement from the list of possible true statements. Sometimes eliminating incorrect answers greatly simplifies identifying the possibly correct ones.

Answer 8

i'm saying all of the statements above are generally false

Answer 9

which is why i said this question makes no sense at the first place. Either that or there are more information that the asker left out.

Answer 10

i am confused as to what it means to say that a function "has no concavity" at a point

Answer 11

like asking if a function is "increasing" at a point