How Do I Find the Point of Inflection in a Cubic Graph?

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To find the point of inflection in a cubic graph, the second derivative must equal zero, indicating a change in concavity. This occurs when the second derivative is positive on one side of the inflection point and negative on the other, meaning the curve transitions from concave upward to concave downward or vice versa. The first derivative's sign change indicates a shift in the gradient. Definitions for convex and concave curves clarify that a convex curve is one that bends upwards, while a concave curve bends downwards. Understanding these concepts is crucial for effective curve sketching.
garyljc
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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
 
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?? Using the definition- that the second derivative is 0 and the first derivative changes sign there.
 
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
 
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.
 
i was wondering if there's an definition for convex and concave ... is there ?
 

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