First Derivative Test, Local Extrema, Examples - Calculus

This video explains the steps and gives the definition of the first derivative test for local maxima and minima, local extreme values of functions or relative extrema. A positive or negative first derivative tells us if a function is increasing/decreasing and identifies critical points. 1st, 2nd and 3rd derivatives of functions like trigonometric ones are calculated in a similar way and a table is typically used for common derivatives. The second derivative test will be covered later on. A worksheet (PDF) of problems with solutions is provided for practice.

📌 Worksheets are provided in PDF format to further improve your understanding:

- Questions Worksheet: https://drive.google.com/file/d/1-6NeYDqLKVXwGn2cLGddt-RgPwE6BRkS/view?usp=drive_link
- Answers: https://drive.google.com/file/d/1ZcFgkcsWJvJAyThTUTCfGbEP0LqGLGtx/view?usp=drive_link

📌 Chapters on What You’ll Learn:

00:00 Determine if a function is increasing/decreasing using the first derivative
01:11 Critical points
01:24 First derivative test
02:38 Worked example

📌 Perfect for calculus students and exam preparation, this tutorial uses plenty of examples and easy-to-follow explanations.

👉 Make sure to check out our full Calculus 1 and 2 course playlist, which covers differentiation, integration, sequences and series and their applications!

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