Learn how to use the second derivative test to determine relative extrema

👉 Learn how to find the extrema of a function using the second derivative test. The second derivative test states that if a function has a critical point for which f'(x) = 0, and the second derivative is positive, then the function has a minimum point at that point. If the second derivative is negative, then the function has a maximum point at that point and if the second derivative is zero, then the function has an inflection point at that point.

To find the extrema of a function using the second derivative test, we first find the derivative of the function and equate it to zero. Then, we solve the resulting equation for x to get the critical points. Then take the second derivative of the function and substitute each of the critical points into the second derivative. The critical points for which the second derivative is positive represent minimum points, the critical points for which the second derivative is negative represent maximum points, while the critical points for which the second derivative is zero represent inflection points.

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Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR

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Видео Learn how to use the second derivative test to determine relative extrema канала Brian McLogan