Understanding the Second Derivative

[Chase.]

I'm having trouble thinking about the second derivative. I've been thinking of it as the rate of change of the rate of change, but that seems to have gotten me into some trouble.

This is a quiz question that I had:

http://i.imgur.com/WUMqY5C.jpg

Ignore the first part, as it should read f' < 0. This leaves only point A and B. I chose B since although the rate of change is negative, it's not accelerating or decelerating. It looks to be remaining rather constant. I think the correct answer is A, which doesn't make sense to me - the rate of change is decreasing, but it's decreasing faster and faster around the A point.

Can someone help me understand this concept?

 

[Dick]

I'm having trouble thinking about the second derivative. I've been thinking of it as the rate of change of the rate of change, but that seems to have gotten me into some trouble.

This is a quiz question that I had:

http://i.imgur.com/WUMqY5C.jpg

Ignore the first part, as it should read f' < 0. This leaves only point A and B. I chose B since although the rate of change is negative, it's not accelerating or decelerating. It looks to be remaining rather constant. I think the correct answer is A, which doesn't make sense to me - the rate of change is decreasing, but it's decreasing faster and faster around the A point.

Can someone help me understand this concept?

B sounds correct. The answer on the quiz may be wrong.

 

[Chase.]

I'm not sure that A is the correct answer, but it was what a lot of other people picked. And if I'm not mistaken, isn't the second derivative the point of inflection? I think A better fits that profile.

 

[eumyang]

Looks like to me that the answer is point B. Between A & B the graph is concave downward, and between B & C the graph is concave upward. The point of inflection is where concavity changes between upward and downward (or vice versa).

EDIT: I edited this post after I saw the previous responses.

 

[Chase.]

Oh you're right... the point of inflection is point B. This obviously isn't the exact graph that was on the quiz but I tried to do a good depiction of it. I hope that B was the actual point of inflection.