WEBVTT
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in this problem, It is given that the graph
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of F is given stayed with reasons, the number
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at which F is not different shape. So for
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the first card we can see here the F is
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not that is function F is not differentiable. It
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X is equal to-4. Okay, see them
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, you can right here at is equal to You
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can see your-40. Great boy, because open
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point is senior at X is equal to zero.
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Can you see here? Yes. So, this
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this shows that this is an undefined point. So
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when the graph breaks then it is not different shape
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letter right? And there becomes a discontinuity on stop
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. Mm Has this continued to this continuously? Right
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. All right. So now we can say at
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X equals two minus for a sharp turn is present
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. Right? So for the sharp turn we cannot
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differentiate it. Oh right, so now for this
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second part second graph we can see here, F
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is not differentiable at X is equal to minus one
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and FZ equals 2-2. I'm sorry. Uh
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X equals two minus two minus one and ex Z
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equals two. Two. So, similarly from here
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, we can see this was-4. Right,
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this was zero. Similarly here, we can see
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a Sharpton, Right? At XX equals to two
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. So this is not different tables. Right?
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So this is the reason for the xxi, closer
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to it is not different people again At x equals
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2-1, X equals 2-1. Here.
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They graph is breaking, you can you can see
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here like this, this is not a point right
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here, like you can in first year as you
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can see this is a point filled with and this
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is not a bank point. This is a break
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off the point, right? So we cannot say
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this is this is also breaking, this is also
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breaking, right? This is also breaking. So
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we cannot say this is a point. So that's
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why this is not a different shape right now.
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Moving ahead, we can see Now for the 3rd
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graf. So it is no different table at x
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equals two. So I'm sorry x is equal to
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one. So this is not differentiable again, this
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is a sharp gun, this is a sharp turn
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. So this is not the friendship. I'm jane
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. And also the graph breaks. Uh and we
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can say this is uh this graph is also spread
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it over minus infinity to infinity. We cannot different
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the points here. So that's why this is not
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different. She able right? No, for the
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4th and the last what we can see here it
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will be. This is the graph. Okay,
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so f is not different shape. X is equal
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to-2, one and three. So minus two
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, one and three. Mhm. So bad.
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Ever A sharp turn is seen. So that is
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not the friendship. So we can see in-2
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-2 and-3-2 and three. It's it's equals
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two minus two. And ecstasy Question my three.
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We can see here the Sharpton. So that's why
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this is not different people. And here if we
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solve this graph we can see in your like this
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that this is this is open point and this is
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also open point, right? This is open,
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this is open, this is open. So the
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points are open here, right? So they can
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say they they start graph breaks which represents the undefined
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value. So if the value is not defined,
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right? So if any of the graph is breaking
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order, you can see if the value is not
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defined uh or you can say this is a spread
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it over minus infinity to infinity. You cannot define
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the function. So this is how we solve this
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problem. I hope you understood this concept. Thank
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you for watching.