Consider the curve $x=1$ in $xy$ plane. I want to know whether tangent at any point on this curve exist which is $x=1$, or tangent does not exist.
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2$\begingroup$ I might have misunderstood you, but tangent to a constant is that constant itself. $\endgroup$– quapkaApr 20, 2014 at 9:35
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2$\begingroup$ A tangent to a straight line is always the line itself. It exists, and it's the easiest possible! $\endgroup$– geodudeApr 20, 2014 at 9:35
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1$\begingroup$ Intuitively, the tangent line at a point on a curve is the line that the curve "looks like" when you zoom-in really, really, RREEAALLLLYY closely on the point. (If the curve doesn't look like a line up-close, then there's no tangent.) Now, no matter how closely you zoom-in on any line, the line it looks like is the line itself. $\endgroup$– BlueApr 20, 2014 at 13:38
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1 Answer
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a line is tangent to a curve at a point if it passes through the point and has the same slope as the curve at that point. Notice that I didn't define slope. Clearly, $x=1$ is not a function, so it wouldn't be appropriate to define slope as $\displaystyle\frac{\Delta y}{\Delta x}$. Lets just say that the slope is vertical. According to this interpretation the tangent line for $x=1$ is $x=1$
