Derivative at corner point

#1

How can we say that here the derivative of the function max(0, ti) at ti=1 is equal to zero?

#2

Hey @SanchitSayala

Let’s rewrite the function as:
f(ti) = max(0, ti) = {0 for ti < 0 and ti for ti ≥ 0}

So, the derivative for ti < 0 is 0, derivative for ti > 0 is 1 and, it’s undefined for ti = 0. Clearly, the derivative at ti = 1 is 1. If it is said to be zero in the video, tell me the time and I’ll look into it.

Happy Learning!

#3

Sorry for the mistake in the doubt, the function is max(0, 1-ti) so it is undefined at ti=1. At about 16:27 in the video, its written that derivative is 0 at ti=1.
But now that I think of it, seems like it doesn’t matter whether we take the derivative at 1 as 0 or 1 since it won’t have a large effect in overall calculation, if any.

1 Like
#4

Yes @SanchitSayala, you’re right. Also, mathematically it is undefined at that point and it is upto us to select a value for that.

Even the probability of ti being exactly equal to 1 is also very small.

#5

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