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Second Derivative Test

This calculus video tutorial provides a basic introduction into the second derivative test. It explains how to use the second derivative test to identify the presence of a relative maximum or a relative minimum at a critical point. If the second derivative is positive at a critical number - a local minimum is present. If the second derivative is negative at a critical number - a local maximum is present. So to identify the relative extrema, find the first derivative, set it equal to zero and identify the critical numbers. Plug the critical numbers into the second derivative function to determine the concavity of the function to see if its concave up or concave down. If it's concave up - it's a relative maximum. If it's concave down, it's a relative minimum. You can confirm the results of the second derivative test using the first derivative test with a sign chart on a number line. Introduction to Limits:    • Calculus 1 - Introduction to Limits   Derivatives - Fast Review:    • Calculus 1 - Derivatives   Introduction to Related Rates:    • Introduction to Related Rates   _____________________________ Extreme Value Theorem:    • Extreme Value Theorem   Finding Critical Numbers:    • Finding Critical Numbers   Local Maximum & Minimum:    • Finding Local Maximum and Minimum Val...   Absolute Extrema:    • Finding Absolute Maximum and Minimum ...   Rolle's Theorem:    • Rolle's Theorem   ________________________________ Mean Value Theorem:    • Mean Value Theorem   Increasing and Decreasing Functions:    • Increasing and Decreasing Functions -...   First Derivative Test:    • First Derivative Test   Concavity & Inflection Points:    • Concavity, Inflection Points, and Sec...   Second Derivative Test:    • Second Derivative Test   _________________________________ L'Hopital's Rule:    • L'hopital's rule   Curve Sketching With Derivatives:    • Curve Sketching - Graphing Functions ...   Newton's Method:    • Newton's Method   Optimization Problems:    • Optimization Problems - Calculus   _______________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets:   / collections