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X-7 If flx) = 7+21 where is f not differentiable?...

Question

X-7 If flx) = 7+21 where is f not differentiable?

X-7 If flx) = 7+21 where is f not differentiable?



Answers

If $f(x)=\frac{x^{2}-1}{x+2},$ where is $f$ not differentiable?

So we have our function here, X squared minus one over X Plus two, and we're being asked when it is not defensible. So let's observe the denominator here. When is dysfunction undefined when X plus two is equal to zero, so X is minus two. So if X is minus, two year function is undefined, so not defensible at X equals minus two. There's no continuities here. The your function would probably would increase toe infinity plus infinity indefinitely, so you cannot really draw a tangent there.

This is a friendship will function wants to know what the derivative US has. Big F of three X would be so approaching role. That would be F prime love three X 10 times The rate of three x, which is times three. So this is our answer here.

Into this pleasant in this lesson. You answering a true of both question? The question is if fx is the differential, then did the access recalled to F of X plus X. F. Prime of X. So this is true that show it. We use the chair route to prove that. So here we hold. We hold F. Of X. And differentiate Act all this becomes the EX. But the EX then times F. Of X. Then plus oh X times G D X F of X. Okay, so this becomes one. Mhm. This becomes X. F. Prime of X. Right? So that is true. Only if F of X is differential. L some of you will to have this. All right. Thanks for time. This is the end of the lesson.

This problem has a lot of steps. So you stick with me. It may seem like a super easy problem. Um But it's not, we have uh x cubed times alfa Becks. And not only do you have to do the first relative, but you have to do the first road of several times. You know, we have to do the drift of the derivatives anyway. You have a product rule which tells you to take the Um like leave one piece alone and take the derivative of the other. Plus now you take the derivative of the first piece, uh leaving the second piece of lung. But now when I go to take the second derivative, you know, actually do this one in red, you have to do the derivative of each piece individually. And we notice this one is also a product with or you leave alone take the derivative plus now you take the derivative leave alone. But then you also have another product rule right here where you leave alone take the derivative Plus now you take the derivative so be six x. Leave alone. Now, if you wanted to save yourself a little bit of time, you could combine like terms here in the middle Because you have six X squared F prime of X. But you still have a product role there. When you get to the third derivative, I need to write small. This is gonna be your final answer. Um So let's start with this piece product rule again. Leave alone take the directive. So it's the third director there Plus leave alone. Uh Sorry, take the derivative league alone. So we're done with that first one. Now do the next directive where you leave alone take the directive plus take the derivative. Leave alone. So we're done with that one. And now we need to do the directive of this now which is another product rule. Leave alone, take the derivative plus take the derivative uh six X. Leave alone. Now, you might leave your answer like that. Or you could simplify which is what I'm doing right here, because I think you can tell That there is now nine x squares For the 2nd derivative. And then here, I can tell there are 18 x first derivatives, And then that last one is just six times the original function.


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