Curve Sketching - First & Second Derivatives - Graphing Rational Functions & Asymptotes - Calculus

This calculus video tutorial provides a summary of the techniques of curve sketching. It shows you how to graph polynomials, rational functions with horizontal & vertical asymptotes and square roots using the first derivative and the second derivative of the functions.
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 ...
_______________________________________
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www.video-tutor.net/
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When f'(x) = - and f''(x) = - : it is decreasing at an increasing rate
When f'(x) = - and f''(x) = + : it is decreasing at a decreasing rate
I got confused in the beginning too thats what he meant though

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5:19 I think you meant decreasing at an increasing rate (f' = - and f'' = +)

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5:19 decreasing at INCREASING rate?

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@15:40 VA should be -3

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Probably already noted, but you misspoke - f' negative and f" negative, slope is decreasing at an INCREASING rate

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[@user-xq3jq3cf2f]

VA at x=3 or x=-3

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x=-3, your VA will exist on the graph somewhere where the curve does not, since you know the denominator can never be 0, you know that x is -3, not 3. I think he made a mistake haha