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The graph of $ f $ is given. State, with reasons, the numbers at which $ f $ is $ not $ differentiable.
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Calculus 1 / AB
Limits and Derivatives
The Derivative as a Function
Oregon State University
Harvey Mudd College
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
The graph of $ f $ is give…
$37-40$ The graph of $f$ i…
in this problem, It is given that the graph of F is given stayed with reasons, the number at which F is not different shape. So for the first card we can see here the F is not that is function F is not differentiable. It X is equal to -4. Okay, see them, you can right here at is equal to You can see your -40. Great boy, because open point is senior at X is equal to zero. Can you see here? Yes. So, this this shows that this is an undefined point. So when the graph breaks then it is not different shape letter right? And there becomes a discontinuity on stop. Mm Has this continued to this continuously? Right. All right. So now we can say at X equals two minus for a sharp turn is present. Right? So for the sharp turn we cannot differentiate it. Oh right, so now for this second part second graph we can see here, F is not differentiable at X is equal to minus one and FZ equals 2 -2. I'm sorry. Uh X equals two minus two minus one and ex Z equals two. Two. So, similarly from here, we can see this was -4. Right, this was zero. Similarly here, we can see a Sharpton, Right? At XX equals to two. So this is not different tables. Right? So this is the reason for the xxi, closer to it is not different people again At x equals 2 -1, X equals 2 -1. Here. They graph is breaking, you can you can see here like this, this is not a point right here, like you can in first year as you can see this is a point filled with and this is not a bank point. This is a break off the point, right? So we cannot say this is this is also breaking, this is also breaking, right? This is also breaking. So we cannot say this is a point. So that's why this is not a different shape right now. Moving ahead, we can see Now for the 3rd graf. So it is no different table at x equals two. So I'm sorry x is equal to one. So this is not differentiable again, this is a sharp gun, this is a sharp turn. So this is not the friendship. I'm jane. And also the graph breaks. Uh and we can say this is uh this graph is also spread it over minus infinity to infinity. We cannot different the points here. So that's why this is not different. She able right? No, for the 4th and the last what we can see here it will be. This is the graph. Okay, so f is not different shape. X is equal to -2, one and three. So minus two, one and three. Mhm. So bad. Ever A sharp turn is seen. So that is not the friendship. So we can see in -2 -2 and -3 -2 and three. It's it's equals two minus two. And ecstasy Question my three. We can see here the Sharpton. So that's why this is not different people. And here if we solve this graph we can see in your like this that this is this is open point and this is also open point, right? This is open, this is open, this is open. So the points are open here, right? So they can say they they start graph breaks which represents the undefined value. So if the value is not defined, right? So if any of the graph is breaking order, you can see if the value is not defined uh or you can say this is a spread it over minus infinity to infinity. You cannot define the function. So this is how we solve this problem. I hope you understood this concept. Thank you for watching.
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