Originally Posted by
angel.white I can't, and I really want to know, it may be a misconception on my part, but when I was thinking about it, I figured two different shaped curves could touch the same point, giving each a different tangent line. I figured if they were circles, they would have the same tangents, but since they weren't, they wouldn't.
If I had to guess at an answer, I'd say it's because they don't cross each other, if they could cross each other they could clearly touch the same point with different tangent lines. But, thats just a guess.
Also, how would you solve for x at this point? I can see that the point would be $\displaystyle (\frac{1}{4}, \sqrt{e})$ But I don't know how to solve for it without just being able to "see" the answer.