► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Critical points are one of the best things we can do with derivatives, because critical points are the foundation of the optimization process. Optimization is all about finding the maxima and minima of a function, which are the points where the function reaches its largest and smallest values. And if we know which values maximize function and which ones minimize it, that has all kinds of real-world applications.
In order to find critical points, which are the points where the function might have extrema, we just take the derivative of the original function, set that derivative equal to 0, and then solve that equation for x. That gives us the critical points of the function. Then, we can test those critical points to determine whether they represent maxima, minima, or neither.
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If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
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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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