Shyanna N.

asked • 01/23/14

the inflection point of f(x)= -2(x-4)^3 +11 is where

I also need to know the end-behavior. for example- x----> + or - infinity 

2 Answers By Expert Tutors

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Kevin R. answered • 01/24/14

K-12/Math/Engineering/Spanish Tutoring

Shyanna N.

That makes a lot of sense, does the graph always look like that to an odd power? Additionally, what is the inflection point?  
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01/24/14

Kevin R.

Yes you are correct. If you go to the website 
 
(http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/Investigating%20Parent%20FunctionsUsing%20GeoGebraGeoGebra%20is%20graphing.htm)
 
you will see the relationship. All even power functions will look like a parabola and all odd power functions will look like a twisted parabola. (Just note that the higher the power the longer the line will be "flat" in the middle)
 
As steve mentioned above. The point of inflection is when the second derivative of the function is equal to zero [ f''(x) = 0 ]. A quick way to check is that the point of inflection is usually (not always, but typically) right in the middle of where the graph goes flat. 
i.e.
\
 \_____
      ^   \
     POI  \
 
 
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01/24/14

Steve S. answered • 01/24/14

Tutoring in Precalculus, Trig, and Differential Calculus

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