► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Inflection points are points at which a function changes concavity, from concave up to concave down, or vice versa. To find inflection points, we'll need to find the second derivative of the original function, and then set it equal to 0 and solve for x. This will give us any possible inflection points of the function.
Once we have the potential inflection point(s), we can use the second derivative test to verify that the function is concave up on one side of the inflection point, and concave down on the other. If concavity is different on either side of the point, then we've confirmed that the point we found earlier is in fact an inflection point. Otherwise, if concavity is the same on either side of the point, then the point is not an inflection point.
Using this method we can also find all of the intervals on which the function is concave up, and all of the intervals where it is concave down.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: optimization,concavity,concave ,educational,calculus expert, derivative test, ,inflection points,derivatives,calculus,concave ,expert,Krista King
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