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

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SUMMARY

The discussion focuses on identifying the point of inflection in a cubic graph through the analysis of derivatives. The key method involves determining where the second derivative equals zero, indicating a change in concavity. The participants clarify that a positive second derivative signifies a convex upward curve, while a negative second derivative indicates a concave downward curve. Understanding these concepts is essential for effective curve sketching and analysis.

PREREQUISITES
  • Understanding of first and second derivatives in calculus
  • Familiarity with the concepts of concavity and convexity
  • Basic knowledge of cubic functions and their properties
  • Experience with curve sketching techniques
NEXT STEPS
  • Study the definition and properties of inflection points in calculus
  • Learn how to calculate first and second derivatives of cubic functions
  • Explore graphical representations of concave and convex curves
  • Practice curve sketching with various cubic equations
USEFUL FOR

Students learning calculus, mathematics educators, and anyone interested in mastering curve sketching techniques for cubic functions.

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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