Maxima and minima on a CLOSED interval (KristaKingMath)

► My Applications of Derivatives course: www.kristaking...
The process for finding the extrema on a closed interval is the same as the process for finding extrema on an open interval. You'll take the derivative of the function, and then set the derivative equal to 0 to solve for critical points.
Because you're looking at a closed interval, you should only consider the critical points within the interval. Any critical points outside the interval can be ignored.
Then you'll use the first derivative test to characterize the critical points inside the interval, and both endpoints of the interval. Because the interval is closed, you can call the critical point or endpoint with the highest value the global maximum, and you can call the critical point or endpoint with the lowest value the global minimum. All other critical points or endpoints will be called local maxima and local minima, which of course will be the local extrema of the function on the closed 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?!”
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[@pureuncutlakers1010]

Always good videos. I have a B.S. in mechanical engineering technology so I was a little light in calculus and I reference your clips all the time. In time I will show my daughter these videos. First off, they are great tools. Secondly and maybe more importantly, I think this world still implicitly discourages women from math, engineering, sciences, etc. It would be great for her to see a woman doing it so well.

[@anuruddhalakshan9023]

Thank you so much Krista,,,, to tell the truth,, i had not been able to understand the difference between the relative extreme and the absolute extreme until i watched this video,,but now i know the difference,,,so,,once again,,thank you so much.

[@AmmarZed]

Oh wow, we talked about this today in class. Amazing timing!

[@kristakingmath]

***** Great!

[@meeras6757]

Nice

[@BenniMurphi]

Love you 😘