Question

Calculus question, multiple choice:
I have the answer, would someone please check it?
Thanks much!

Answer 1

Let f(x) be a polynomial function that f(4) = -1, f ' (4) = 2, f '' (4) = 0. If x < 4, then f '' (x) < 0 and if x > 4, then f '' (x) > 0. The point (4,-1) is a _____________ of the graph of f.

Answer 2

relative maximum

relative minimum

critical number

point of inflection

none of these

Answer 3

I am almost certain that the answer is 'point of inflection'
Would someone mind telling me if I am correct?

Answer 4

because if x<4 then f'' <0 means points are going up
if x>4 f''>0 points are going down
the concavity switches
so it is a p.o.i. ?

Answer 5

Yes - if the second derivative changes sign on both sides of x=4, then you have a point of inflection. The first derivative is positive so the function is increasing at x=4, so it could look like this:

Answer 6

ok thank you very much!

Answer 7

oh and thanks for the graph too!
you get a medal, question closed. :)