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I was given this question: Find the tangent through point (1,-1) of y^2 = x^3 -2x + 2. After some time i found out that this is (x-3)/2. But the b) part of the question was: the curves intersect at another point, find this? And i couldnt because setting both equations equal to each other gives me 1,-1 again..? Thank you!
If, then
so that at (1, -1), -2y'= 1 and y'= -1/2. No, (x- 3)/2 is incorrect because that has slope 1/2, not -1/2.
Yes, one solution is (1, -1) again but that will be a quadratic equation so there may be another solution.
Your first question makes perfect sense. But the second is completely mysterious to me. What curves (plural)? The answer above is one interpretation - namely, find a second point where the tangent line intersects the curve. By the way, there are several good free or inexpensive graphing programs available, Geogebra and Graph, for example. A little time spent "checking your work" with such a program is far faster than online help. I rapidly created the following:
Attachment 26436
The second curve is the straight line.
