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Gradient question - Exam 2018

Hi! I can't understand the logic of problem 10 in 2018 exam.
The question is: for which x does the function has a sub gradient, and I thought that a subgradient existed for any x, considering that the function is continuous, while the answer is that a sub gradient can be found only at x=2 and x=3. Could someone explain me why? Thanks!

Hey! From what I understood, a sub-gradient must always be below the function. So if you try to draw a straight line in the other points you'll find out that no matter what, that line is going to intercept the function and go above it. Hope this helps.

Hi, I still don't understand this.. despite the answer. When you say straight line do you mean horizontal? Also I don't get how it works in this case because a straight line of value 2 is going to be above the function right? Thanks in advance

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