► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Figuring out where a function is increasing and decreasing is part of any optimization problem. A function is increasing wherever it is moving up as you move from left to right. A function is decreasing wherever it is moving down as you move from left to right.
If we want to figure out where a function is increasing and decreasing, we need to take the first derivative of the original function, then set it equal to 0 and solve for x. This will give us the potential critical points of the function, which are the points at which the function may change direction from increasing to decreasing, or vice versa.
In order to characterize the function's increasing/decreasing behavior, we have to use the first derivative test to test each interval between the critical points. If the values we test on either side of the critical point return a positive value, then the function is increasing on that interval. Otherwise, if the result is a negative value, then the function is decreasing on that interval.
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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: decreasing,increasing,derivatives, ,optimization,expert,increasing decreasing,educational,Krista King,calculus,critical points,calculus expert, derivative test
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