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There is nO tangent line t0 the graph of y = 22 which passes through the point (1,5)- (Hint: proof by contradliction: Also_ SOlL will need tO rememeber some caleulu...

Question

There is nO tangent line t0 the graph of y = 22 which passes through the point (1,5)- (Hint: proof by contradliction: Also_ SOlL will need tO rememeber some caleulus to do this probler:

There is nO tangent line t0 the graph of y = 22 which passes through the point (1,5)- (Hint: proof by contradliction: Also_ SOlL will need tO rememeber some caleulus to do this probler:



Answers

Equation of a Tangent Line Find an equation of the tangent line to the curve at the given point. Graph the curve and the tangent line. $$ y=\frac{x}{x-1}, \quad \text { at }(2,2) $$

Everyone. Today we're going to solve a problem. Number 20 way off. 2.1 equal to 2.1 square, which is equal to 4.41 Emma kowtow to into 2.1, which is four point why minus 4.41 equal do 4.2 in tow. X minus 2.1. Why you could do 4.2 x minus four point forward. That's the window for a question. Thank

Any time you're asked to find the equation of the tangent line, all you need is a point in a slope. I'll get to that here in a second. Will they give you a point? So you don't even have to do the arithmetic arithmetic there Now, the slope, then Well, that means finding the derivative when X equals two and all they give you the problem is that why equals e to the name of two X plus x square to this is kind of complicated. Um, Now, you could have done the math to figure out all they had to do is give you the excess too, because if you plug in to hear, you would get negative four plus 40 on E to the zero power is one. So they even have to give you that point. But what you have to find only such colors is the derivative. So the drift of of this is stays the same, but then multiplied by the derivative of that numerator, which is negative. Two plus two x eso. Now what we have to do is plug in X equals two here, here and here. And that's why it was actually worthwhile. Like to notice that this is just the same as the Y coordinate which we found earlier was one. So now all you have to do is figure out that two times two is four nave to plus four is too. So the slope at that point is to So why am I saying all you need is a point and a slope is You probably remember point slope form from an earlier math class. That was why minus the y coordinate equals the slope and then expands your extra coordinate. And most professors prefer, um, the answer being solved for Why? So I would stop right here. But this math isn't too hard to simplify to the distributive property. So would be to X and B minus four plus wannabe minus three. I'm just double checking my work before stopping. I'm pretty sure I am good. So you might have to take this step further

Bolivia going to star program about 16. Yeah, eh, Makoto two in minus 1.5, which is equal to minus three. So by minus two point toe fight equal to my industry. Express one point, but vehicle to minus three X minus 2.25 That's the end of a question. Thank you.

The equation of the tangent line of why it was x squared when x equals 2.1. So first let's find the slope of the curve which is going to be the same as the slope of the tangent line by taking a derivative. Um With the power rule, we bring the two down in front. The new exploded is one which we don't have to write. So at x equals 2.1. Why Prime is two times 2.1 is 4.2. So the slope of the tangent line is 4.2. Um and to get an equation, we need a slope in a point, we actually don't have a point. Um so at X equals 2.1. We have to find why Why is 2.1 squared, which is 4.41. So now we have the point to .1 comma 4.41 And a slope of 4.2. So then the equation of the tangent line is we can write this in point slope form, which is the easiest way to write down the answer quickly. It might not be easy to do anything else with it. But there we go. There is the equation of the tangent line


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