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anonymous
 4 years ago
At what point does the normal line to the curve y = x^23 at (1, 2) intersect the curve a second time?
The derivative is 2x so the slope at (1, 2) is 2 thus the equation of the tangent line is y+2 = 2 ( x1) which I can graph both of, and am still not seeing where it crosses twice:
http://www.wolframalpha.com/input/?i=y%2B2+%3D+2+%28+x1%29+and+y+%3D+x%5E23
anonymous
 4 years ago
At what point does the normal line to the curve y = x^23 at (1, 2) intersect the curve a second time? The derivative is 2x so the slope at (1, 2) is 2 thus the equation of the tangent line is y+2 = 2 ( x1) which I can graph both of, and am still not seeing where it crosses twice: http://www.wolframalpha.com/input/?i=y%2B2+%3D+2+%28+x1%29+and+y+%3D+x%5E23

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[y = x^2  3\]\[\frac {dy}{dx} = 2x\]\[y' (1) = 2\]\[Y _{tangent}^{} = 2(x1)2\] The normal line to the curve is perpendicular to the curve, so it has the negative reciprocal slope of the tangent.\[Y _{normal}^{} = \frac {1}{2}(x1)2\]So now just set Ynorm equal to y = x^2  3 to find the other coordinate. My tangent and normal line equations are in the linearization form by the way, you can simplify them down if you want.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Negative reciprocal! Geesh. That helps! Thanks!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Hehe, well, now you know :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0err ok so I set 1/2(x1)2 = x^23 and eventually got x^2+1/2x  3/2 which, when I put in 1 for x, I get 0 out which is evidently not correct. I guess I am still confused after all :/

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[Y _{norm}^{} = 0.5x 1.5\]\[Y = x^2  3\]\[0 = x^2  3 + 0.5x + 1.5 = x^2 + 0.5x  1.5\] Solving for that should give you the other solution, which is 1.5. I think you just made a computation error somewhere, no biggie.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh, you put 1 into that... No...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0When you set Ynorm = Y, you are finding when the 2 graphs intersect. Its not the derivative or anything, so you don't plug in 1. You already know that they intersect at the point given to you, (1,2). You just have to find the other point. Solving for that equation will give you x = 1, x = 1.5. So the other coordinate where the normal & the parabola intersects has a xcoordinate of 1.5 Plugging in 1.5 into either equations will give us the y coordinate, which is 0.75. So the other point where the normal intersects the curve is (1.5, 0.75).

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Do you get it, or need a bit more explanation?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm sorry, reviewing now, had a kid wake up with a bad dream _

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you!!! I /do/ understand!! I have no idea how I would've gotten that without your help.
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