# Math Help - Curvature Question

1. ## Curvature Question

I was asked by my teacher "What is the curvature of a 2-D curve at an inflection point? Why?" Can someone help me with this one? I'm absolutely at a loss as how to proceed with this. Thanks.

2. Originally Posted by JonathanEyoon
I was asked by my teacher "What is the curvature of a 2-D curve at an inflection point? Why?" Can someone help me with this one? I'm absolutely at a loss as how to proceed with this. Thanks.
isn't curvature defined in terms of the second derivative? what is the value of the second derivative at an inflection point? what does this say about its curvature?

3. Originally Posted by Jhevon
isn't curvature defined in terms of the second derivative? what is the value of the second derivative at an inflection point? what does this say about its curvature?

Hmmmm... at an inflection point is when the signs change from negative to positive so that means 0 slope which means no curvature. Did I at least close?

4. Originally Posted by JonathanEyoon
Hmmmm... at an inflection point is when the signs change from negative to positive so that means 0 slope which means no curvature. Did I at least close?
what changes from negative to positive? and it is the first derivative that deals with slope, not the second, so no

5. Originally Posted by Jhevon
what changes from negative to positive? and it is the first derivative that deals with slope, not the second, so no

Ok let me try again. At an inflection point is where concavity changes...... soo.... uhhmm may I have another hint?

Edit : Just thought of this but since inflection points are where the concavity changes, wouldn't it be a straight line at that inflection point so that'll mean no curvature at all?

6. Originally Posted by JonathanEyoon
Ok let me try again. At an inflection point is where concavity changes...... soo.... uhhmm may I have another hint?

Edit : Just thought of this but since inflection points are where the concavity changes, wouldn't it be a straight line at that inflection point so that'll mean no curvature at all?
yes, the second derivative is zero at points of inflection, thus we have zero curvature. that's pretty much it

7. Thanks!!!!