Curve Sketching Example | Calculus - JK Math

Example Problems for How to Sketch Curves Using Calculus

In this video we look at an example of sketching the graph of a function using various techniques learned across algebra and calculus. We use a step-by-step process in order to accurately sketch the graph of a function.

NOTE: Unfortunately due to the length of these types of problems involving sketching a graph, there is only one example in this example video. Typically I try to include multiple examples in an example video, but to stay consistent with my promise of each video for Calculus 1 being less than 20 minutes (with the exception of this topic’s lesson), only one example could be completed in that timeframe in a manner that is well-paced and ultimately helpful to the viewer. I may revisit this topic with more videos in the future to make up for the lack of examples.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes!

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 Example Intro: f(x) = x^5-5x
0:15 Domain, Continuity, and Asymptotes
1:49 x-intercepts
3:54 y-intercept
4:43 First Derivative & Critical Values
6:01 The First Derivative Test
8:29 Plotting Relative Extrema
10:22 Second Derivative & Inflection Point
11:15 Concavity Check
13:40 Combining Number Lines
15:33 Sketching the Graph

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-Josh from JK Math

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