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Absolute Extrema on an Interval Examples | Calculus

JK Math

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Example Problems for How to find Extrema on an Interval (Calculus)

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Video Chapters:
0:00 Example 1 - f(x) = x^2+2x-4 on [-1,1]
3:20 Example 2 - f(x) = 8x+3 on [0,6]
5:10 Example 3 - f(x) = x^3-27x on [0,4]
7:32 Example 4 - f(x) = Cubed root of x on [-8,8]
9:35 Example 5 - f(x) = sec(x) on [-pi/4, pi/3]
13:48 Example 6 - f(x) = 2x/(x^2+1) on [-2,2]

📝 Lesson Video For These Examples: Extrema on an Interval | Calculus Lesson 19

⏩ Next Lesson: Rolle's Theorem | Calculus Lesson 20

📺 Course Playlist: Calculus 1

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5 Comments

@JKMath Creator 1 month ago Pinned

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@lucky45-rohit 1 month ago

You deserve more views and likes 😊

@musolesamba5215 3 years ago (edited)

Sir your method of solving is easy to understand

@AylinMuratli 10 months ago (edited)

Thank you so much for working through these problems in an easy to understand manner! I was just wondering though, for Example 4, wouldn't we also check x = 0 as a value since that is where the derivative is undefined? I understand it doesn't end up producing a global min/max but shouldn't we still check it? Thank you!

@ech_o. 5 months ago

Good day. I was just wondering that since the functions will be enclosed to a specific interval, does that make the endpoints to always be relative etrema of the given function on an interval?

I am just wondering since in some cases, the enpoints turned out to be the absolute extrema of the function on an interval. And then there are cases where the critical points are the absolute extrema. Other cases lead to the endpoint to be a critical value as well and is the absolute extrema too. If the critical values turned out not to be the absolute extrema, they are considered relative extrema since tangent slope at their points are 0. But is it the same case for endpoints? Do we consider them relative extrema if they are not the absolute? I hope I am making sense. Thank you in advance for your time!