# Thread: Graphs-identifying concavity and inflection points

1. ## Graphs-identifying concavity and inflection points

a)If this figure is the graph of the second derivative f"(x), where do the points of inflection of occur, and on which interval is concave down?

b) If this is the graph of the derivative , where do the points of inflection of occur, and on which interval is concave down? I know the answer to this one is b,e ;(b,e)

Basically how do I tell?
So if I look at just f(x), the inflection points are the min and max.(?) And concave downwards is just like a downwards parabola

If I look at f'(x), are the inflection points still the min and max? And concave downwards is a negative slope? I'm confused on this part...

And for f''(x)...don't even get me started

Seriously, if anyone can fill in any of this questions...you'd be my favorite person ever!

2. Originally Posted by bcahmel

a)If this figure is the graph of the second derivative f"(x), where do the points of inflection of occur, and on which interval is concave down?

b) If this is the graph of the derivative , where do the points of inflection of occur, and on which interval is concave down? I know the answer to this one is b,e ;(b,e)

Basically how do I tell?
So if I look at just f(x), the inflection points are the min and max.(?) And concave downwards is just like a downwards parabola

If I look at f'(x), are the inflection points still the min and max? And concave downwards is a negative slope? I'm confused on this part...

And for f''(x)...don't even get me started

if the graph is y = f''(x) ...

f(x) is concave up where f''(x) > 0 , concave down where f''(x) < 0 , inflection points where f''(x) changes sign.

if the graph is f'(x) ...

slope of the graph is f''(x). f(x) is concave up where f'(x) is increasing, concave down where f'(x) is decreasing, inflection points where f'(x) changes slope.

3. ## inflection point

Originally Posted by bcahmel

a)If this figure is the graph of the second derivative f"(x), where do the points of inflection of occur, and on which interval is concave down?

b) If this is the graph of the derivative , where do the points of inflection of occur, and on which interval is concave down? I know the answer to this one is b,e ;(b,e)

Basically how do I tell?
So if I look at just f(x), the inflection points are the min and max.(?) And concave downwards is just like a downwards parabola

If I look at f'(x), are the inflection points still the min and max? And concave downwards is a negative slope? I'm confused on this part...

And for f''(x)...don't even get me started

Seriously, if anyone can fill in any of this questions...you'd be my favorite person ever!
An inflection point for $\displaystyle \text{f}(x)$ occurs at a relative extremum of $\displaystyle \text{f}\,'(x)$.

4. ok so for the question a)If this figure is the graph of the second derivative f"(x), where do the points of inflection of occur, and on which interval is concave down?

It's concave down on the interval (d,f) (-infinity, a)
inflection points at a,d,f? (the zeros? because this is where the 2nd derivative changes sign- is this right/)

I really appreciate all the answers, I just want to make sure I understand this and I'm doing it right.

5. Originally Posted by bcahmel
ok so for the question a)If this figure is the graph of the second derivative f"(x), where do the points of inflection of occur, and on which interval is concave down?

It's concave down on the interval (d,f) (-infinity, a)
inflection points at a,d,f? (the zeros? because this is where the 2nd derivative changes sign- is this right/)

... correct

6. ok, thank you so much!