Concavity, Inflection Points, and Second Derivative

This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
_____________________________
Extreme Value Theorem:
• Extreme Value Theorem
Finding Critical Numbers:
• Finding Critical Numbers
Local Maximum & Minimum:
• Finding Local Maximum ...
Absolute Extrema:
• Finding Absolute Maxim...
Rolle's Theorem:
• Rolle's Theorem
________________________________
Mean Value Theorem:
• Mean Value Theorem
Increasing and Decreasing Functions:
• Increasing and Decreas...
First Derivative Test:
• First Derivative Test
Concavity & Inflection Points:
• Concavity, Inflection ...
Second Derivative Test:
• Second Derivative Test
_________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

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maybe a question. Why do we derive twice! We do not equate the first derivative with zero, as in Rolle's theorem.!! Why do we derive twice and not 3 or 4 times?.

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If there's a cusp at a point, and that point is between 2 concave ups, could we include the cusp in the interval of concave up for example a cusp at 0, but the interval of concave up is (-1,2)?

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What if the second derivative is constant? How will we determine the intervals for concave up and concave down?

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idk if you still need an answer but if the constant is a positive number then its concave upwards and if its negative then its concave downwards

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and there are no inflection points so therefor you dont have to determine the intervals of whether its concave up or down

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