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At 1:49, the instructors says that staying within the bounds of (-1,1) slope, means that the function is growing linearly.
Then at 2:08, the instructor shows the following function and says that it grows linearly:
This function doesn’t look linear to me as its gradient is not constant, and changes sign as well.
What does the instructor means by the function growing linearly?? Please help.
Good question! I have to admit I never noticed she said that - and I’m not sure, either, why she used those words. You’re right, the curve is not growing linearly. I did notice that the second time she says, “the function never grows more than linearly” - so I’m guessing that she was thinking about those lines that are drawn with a slope of 1 and how the function should have a slope that’s less than that, and then she just made an unfortunate choice of words to summarize that.
Anyway, the main point is that for 1-L continuity, the slope should change slowly - with absolute value of the slope less than 1. You can ignore that mention of “growing linearly”
Thank you! I was actually confused as to what that meant and was searching internet as to what linearly meant in this context. I am still learning a bit of mathematics so I wasnt sure what it meant in this context. Thank you for clarifying that the instructor just meant that “the function never grows more than linearly”.
