► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course

The critical points of a function are the points at which the function changes direction from increasing to decreasing, or vice versa. Critical points are valuable because they will be the points at which the function has a local or global maximum, or a local or global minimum. In other words, the extrema of a function will always be located at critical points, so if we can find the critical points of a function, we'll also be able to find the function's extrema.

Luckily, to find critical points, all we have to do is take the first derivative of the function, set it equal to 0, and solve for x. This will give us any potential critical points. The tricky part is that the points we find with this method are only potential critical points. In order to prove that they are in fact critical points, we have to prove that the function changes direction at those points, which we'll do using the first derivative test.

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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

● ● ● CONNECT WITH KRISTA ● ● ●

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: increasing,critical points, ,calculus expert,expert,optimization,calculus, derivative test,educational,derivatives,Krista King,decreasing,increasing decreasing

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