Curve Sketching With a Slant Asymptote - A Step by Step Example Using Calculus
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This video presents four steps
This video presents four steps that can be used to graph a rational function. Those four steps are then applied to sketch the graph of a rational function with a vertical and slant (or oblique) asymptote.
0:00 - Introduction
1:13 - Step 1: Identify All Asymptotes
6:40 - Step 2: First Derivative and Critical Bumbers
16:15 - Step 3: Second Derivative and PPI
24:12 - Step 4: Sketch the Graph
To graph a rational function you need to know how to apply the quotient rule, have an understanding of asymptotes, and know how to express intervals using interval notation. More information about these topics can be found below:
Types of Asymptotes: Calculus - Curve Sketching - Types of...
Finding Vertical Asymptotes: Calculus - Finding Vertical Asymptotes
Finding Horizontal Asymptotes: Calculus - Finding Horizontal Asymptotes
Finding Slant (or Oblique) Asymptotes: Calculus - Finding Slant (Oblique) As...
An Easy Way to Remember the Quotient Rule: The Quotient Rule Rhyme - An Easy Way...
Find a derivative with the Quotient Rule: Calculus - Using the Quotient Rule to...
Finding a Second Derivative with the Quotient Rule: Calculus - Finding the Second Derivat...
Using Interval Notation: Interval Notation
If you have any questions, feel free to ask in the comments section.
0:00 - Introduction
1:13 - Step 1: Identify All Asymptotes
6:40 - Step 2: First Derivative and Critical Bumbers
16:15 - Step 3: Second Derivative and PPI
24:12 - Step 4: Sketch the Graph
To graph a rational function you need to know how to apply the quotient rule, have an understanding of asymptotes, and know how to express intervals using interval notation. More information about these topics can be found below:
Types of Asymptotes: Calculus - Curve Sketching - Types of...
Finding Vertical Asymptotes: Calculus - Finding Vertical Asymptotes
Finding Horizontal Asymptotes: Calculus - Finding Horizontal Asymptotes
Finding Slant (or Oblique) Asymptotes: Calculus - Finding Slant (Oblique) As...
An Easy Way to Remember the Quotient Rule: The Quotient Rule Rhyme - An Easy Way...
Find a derivative with the Quotient Rule: Calculus - Using the Quotient Rule to...
Finding a Second Derivative with the Quotient Rule: Calculus - Finding the Second Derivat...
Using Interval Notation: Interval Notation
If you have any questions, feel free to ask in the comments section.
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