Curve Sketching

Apr 2010
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0
Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.
 

mr fantastic

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Dec 2007
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Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.
It follows from the definition that the x-coord of the point of inflection occurs where dy/dx has a turning point.
 
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HallsofIvy

MHF Helper
Apr 2005
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Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.
Sounds straightforward to me. An inflection point occurs where the second derivative is 0. Set the second derivative equal to 0 and solve for x. Then calculate the first derivative for that x.
 
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