Use the graph of g in the figure to do the following.

Question

b. Find the values of x in (-2,2) at which g is not differentiable.

Accepted Answer

Welcome back everyone. In this problem, we want to determine the values of X in the interval open parentheses -3, 3 closed parentheses, at which F is not differentiable using the following graph. A says F is not differentiable at the point where X equals -2, 0 and 1. B says at -1 and 0, C at 0 and 2, and D at -10 and 1. Now how can we figure out at which values of XF would not be differentiable? Well, there are 3 conditions that can either be met for a function F to not be differentiable, OK, at a point C. So F is not differentiable at a point where X equals C if first of all. The function F is not continuous. At sea And know the function if it's not continuous at C if it meets any of the three following criteria. First, if F of C is undefined. If the limit Of FFX as X approaches C does not exist, OK. And third, if the limit of F of X as X approaches C is not equal to F of C. So if any of these criteria are satisfied, F is not continuous at C and thus it will not be differentiable. Next, it's not differentiable if F has a corner at C. Meaning the slopes or the derivatives of f from the left and right sides of C are not equal. And third, a function F is not differentiable if F has a vertical tangent. At sea. I know that makes sense because the slope of a vertical tangent is undefined, but to differentiate, the derivative has to have a finite value. So no, if our function does not meet any of these values at a certain point or any of these criteria, then it is not differentiable at that point. So let's take a good look at our graph to see if it fits any of these. Let's go to some usual suspects. Let's go to some points where it seems that it would not be differentiable. Now, let's jump to where X equals -2. It looks a little suspicious because there's a hole here. Now, at this point, is F differentiable? Well, let's go to our, let's go through our list, OK? So now at X equals -2, notice there that there's a hole, no other solid point. So this tells us that F of -2 is undefined, OK? And since it's undefined, that means FF 2 F of negative 2. Oh sorry, F is not continuous at X equals -2, based on our first criteria, OK? So F is not continuous. OK. At X equals -2, which means it is not differentiable. It's not continuous, it's notable. Now let's go back to our graph. So we know that this is one point that we already have. Now, again, if we are looking for some suspects here, it looks like something suspicious is going on here at the point where X equals 0, OK? So is our function differentiable at X equals 0. Well, let's test it with our first criteria. Let's first check if it's continuous, OK? And know at X equals 0. For starters, we know that there's a solid, solid point here where, where F of X equals 6, OK? So that means that F of 0 is undefined, OK? But if we look at our limit from the left and right hand sides, OK, if we take the limits from the left and right-hand sides where X equals 0. Notice that Or a limit of FF X. As X approaches 0 from the left is equal to 2, if we go back to our diagram, OK. And if we go again on our graph, notice that the limit as X approaches 0 from the right of F of X, OK, is equal to 6. So what does this tell us? Well, no, this tells us then, OK. So it's right out here. Therefore, the limit, OK, as X approaches 0 from the left of F of X. is not equal to the limit as x approaches 0 from the right of F of X. So thus, OK, that means the limit. Of F of X as X approaches 0 does not exist. If the limit does not exist, that means it is not continuous and thus F is not differentiable at X equals 0. Now let's go back to our graph. Are there any other points? We'll notice here that there's a point, there's a corner, sorry, where X equals 1. Remember that if F has a corner, it is not differentiable because that means the slope from the right will not be equal to the slope from the left. OK. So thus at X equals 1, OK. Add X equals 1. It has a corner, and because it has a corner, that means it's not differentiable. Thus, F is not differentiable at X equals -20 or 1. If we look back at our answer choices, that means A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Use the graph of g in the figure to do the following. <IMAGE>
b. Find the values of x in (-2,2) at which g is not differentiable.

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Use the graph of g in the figure to do the following. <IMAGE>b. Find the values of x in (-2,2) at which g is not differentiable.

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Use the graph of g in the figure to do the following. <IMAGE>
b. Find the values of x in (-2,2) at which g is not differentiable.