# Curve Sketching

1. Jan 29, 2008

### garyljc

Hey guys ,
I'm currently learning curve sketching
and i was thinking ... what would be the best approach towards finding the point of inflection in a cubic graph . Any suggestions ?
Thanks

2. Jan 29, 2008

### HallsofIvy

Staff Emeritus
?? Using the definition- that the second derivative is 0 and the first derivative changes sign there.

3. Jan 29, 2008

### garyljc

What do you mean by changes sign ?
I do understand that the sign change in the first derivative means the gradient
the second derivative means whether the curve is concave or convex ....
that's all i know about the signs so far..
do you mind elaborating more ?
thanks

4. Jan 29, 2008

### HallsofIvy

Staff Emeritus
My mistake, I meant that the second derivative changes sign there: is positive on one side of the inflection point and negative on the other. Yes, second derivative positive means the curve is "convex" upward and second derivative negative means the curve is "convex" downward ("concave" upward). At an inflection point the concavity changes.

5. Jan 30, 2008

### garyljc

i was wondering if there's an definition for convex and concave ... is there ?