Summer of Math Exposition

A nice clean list of step by step instructions on how to draw the graph of a given function. While the video doesn’t do anything mind blowing, listing the steps and working through an example, can be a solid guide for any high- schooler currently facing this chapter of their maths journey.

The video actually let me (know nearly nothing about calculous) understand how this method work. I always like to make do some math that is easy for computer but hard for human, like calculate logarithm by hand, and this video actually broaden my horizon as I don’t even know this is possible before

really a treasure for those who is very weak in constructions and not familiar with graphs and curves

I enjoyed this video

I think this is a really solid demonstration of a lot of these topics from the start of calculus, and I’m sure that even just the animation of it can do some good - well done.

That said, I do have to say, it’s just a bit… vanilla, if that makes sense. I think there are some opportunities in this process to provide insights that a lot of students don’t typically get to hear: for instance, getting further into why local extrema occur when the derivative is 0 or doesn’t exist, why we can just pull any points we want from each interval in the sign chart to get a representation of the sign for the whole region, and how that relates to the intermediate value theorem, or even just why the 1/0 behavior gives us a vertical asymptote. There’s always further depth to be found in those details, and they can bring a new dimension of clarity to what’s happening here, and I think you mainly stuck to what was strictly necessary to get the answers you needed. Which possibly is wise for the type of video this is, it might mean that the length is something more palatable for a classroom demonstration for instance - there are pros and cons to any decision like that. I just think that there are some places that the explanation could be elevated to the next level if that was your goal.

This is a very useful skill. I like how you found a way to break it down into learnable concepts. I feel like playing around with Desmos is still valuable, but this method can give people a head start and solidify some ideas.

Very nice one. Number line is an excellent example to use. My suggest is that the video can give more examples without using number lines as advanced students are not using number lines but something else.

I liked how this explained a topic usually taught very poorly in a calculus class, and I think that if this was my introduction to curve sketching, I would’ve understood it much better.

This is a good overview of curve sketching, and you do a good job explaining each feature to look for. But you only put them together at the end, which means the audience has to keep everything in mind until then. It might make sense to have a running sketch of your example function and add each feature after you explain it.

It’s a fine video. The video is clear and easy to follow. The main animations make the video smooth, but the visuals themselves aren’t the most inspiring (i.e clean execution but plain design).

The video does its job and it would be useful in a class setting. I wouldn’t say it’s novel or memorable. But I would say it’s better than the average video.

Congratulations on posting your first video and I hope this is only the beginning of a very exciting journey for you in content creation. Curve sketching is a standard topic in Calculus 1, and I believe you went through all the key points well. I can imagine a student making a curve sketching cheat sheet by covering all the points you did in this video. The reason for my score is also because it’s a standard topic. It’s well done, but it’s also been well done by many other textbooks and web sites.

This one took me back to high school! Lots of great stuff in here, with clean animations and consistent pacing.

The biggest thing I would conceptually suggest overall, to really elevate this and leave viewers with a lasting impression, is to leverage the power of these animation tools to show several examples of these graphs and build intuition on how to reason about their structure. As it currently stands, the video is more heads-down on a particular example, with the actual sketching happening at the very end. We see some quick visuals of a few of the features we’re identifying, but it’s more focused on following the rote steps to process a written equation and then turning it into a graph at the end.

This is similar to how it was taught to me back in high school, but it would be amazing to take an example like that (x^2 - 1)/x^3 and show how it relates to the graphs of its numerator and denominator (which students will likely have a much easier and faster time visualizing). I think this could help alleviate the mental block students face when asked to sketch a graph of a “scary-looking” or complicated function like this. All the tools you presented are excellent for refining the estimate, but making a super quick 15-second back-of-the-napkin sketch using intuition is an incredibly valuable skill to practice!

For example, explaining why an even*odd or even/odd is odd would be a cool addition to help facilitate this. This would immediately tell us that our plot should be rotationally symmetric just by recognizing that x^2 - 1 is even and x^3 is odd. And you could show lots of other examples of even and odd functions and compositions of them along the way so we can get a feel for what they look like—I know you mentioned some at the end, but it could be interspersed throughout.

Good stuff, excellent reference/refresher for confused calculus students, and with a few pedagogical refinements it could be fantastic!

This is a very nice explainer! The topic choice is very practical, the lesson is very clear, and the visuals pair very well. You do go very fast through algebraic details, but you also did a good job of communicating why you were doing this and how the viewer should direct their focus. Overall, great work.