# Homework Help: Points of Inflection

1. Mar 20, 2013

### Chase.

I'm supposed to identify the points of inflection in the following graph:

I know the point of inflection is where concavity changes, and I keep getting stuck on one answer that is apparently not correct.

I believe that the following points are points of inflection: ABCDEFHJKL

A - f'' transitions from decreasing to increasing
B - f" transitions from increasing to decreasing
C - f" transitions from decreasing to increasing
D - f" transitions from increasing to decreasing
E - f" transitions from decreasing to increasing
F - f" transitions from increasing to decreasing
H - f" transitions from decreasing to increasing
J - f" transitions from increasing to decreasing
K - f" transitions from decreasing to increasing
L - f" transitions from increasing to decreasing

Can someone tell me where I went wrong?

2. Mar 20, 2013

### Staff: Mentor

For the most part, that is incorrect. You have listed all of the points, and some of them actually are inflection points, but not all of them.
I don't think you have a good understanding of what an inflection point is. In your own words, what do you think an inflection point is?

At point A, f'' is NOT transitioning from decreasing to increasing. f is changing from decreasing to increasing. What does that tell you about f' at A? Can you look at the graph around point A and say something about f''?

3. Mar 20, 2013

### SammyS

Staff Emeritus
At A, the curve is concave up both to the right and to the left. Also it's the first derivative that changes from being negative to being positive, but that means that the second derivative is positive because the first derivative is increasing.

4. Mar 20, 2013

### Chase.

I see my mistake. I only have one submission left so I want to make sure that I'm correct.

At point B the concavity changes from up to down. Also at H, it changes from concave down to concave up, but I know that B and H are not the only points because I attempted that solution earlier. Can someone give me a hint as to what I am missing?

5. Mar 20, 2013

### Staff: Mentor

Now you're on the right track. Look at each of the listed points and decide whether the concavity is changing from concave up to concave down or vice versa. There are more than two inflection points.