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Problem 28 Easy Difficulty

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ x^2 + 2xy + 4y^2 = 12, (2, 1) $ (ellipse)

Answer

$y=-\frac{1}{2} x+2$

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Video Transcript

Ms Problem. Where's to use instant differentiation? Finding question, going to line up a teacher and given point to one. All right, you know that the question of tension lines will be your wine one. So I'm not busy with territorial dysfunctional bullet at a given point. What Spike by X minus X Not where? Why not? Is one the next, not is two. So we need to point their bitter in order to do that. Less activity or both sides With respect, X, we have two X plus or diss term will be using protocol to one plus two extends for crime plus age White on white crime Z zero. Now, let's pluck given, uh, eggs and one in order to fund derivative at this given points in order to find this term, um, we have two times two plus two times one plus two times two. Why prime plus a 10 4 times. Why? Prime is zero firmness. We see that that white prom should be negative. Six over 12 on. That is a negative one. Health. Now we have everything that you need. Then we can right? You crazy a pendant, Linus, Why? By this point which is. Why not? Times there were terminated one hell, Well, why buy X ones too homeless? We see that the question of standard line is that two minus X or two.