Is it possible to plot a function with a vertical tangent line while the plot of the function has no vertical line segment?

Question

You should perhaps be a bit more careful with your choice of words. A "derivate" or a "function" cannot be a "line", those are different concepts. I suspect that what you are asking is whether the tangent line to the graph of a function can be vertical at a point? (What you mean by the function itself being a vertical line, or a step function having vertical slope, I don't know, however...) — Hans Lundmark, Dec 11 '20 at 10:29

score 1 · Accepted Answer · answered Dec 11 '20 at 07:12

1

Yes, eg- x^(1/3) (real to real only not complex) and has a vertical tangent at x=0

answered Dec 11 '20 at 07:12

Mehul

If I take the derivative of the function, I get a function with $x$ in the denominator. I think that would make the derivative undefined at $x=0$, but I am not absolutely sure. – Christina Daniel Dec 11 '20 at 07:18
Yes the derivative is undefined, but you yourself asked for it right? – Mehul Dec 11 '20 at 07:26
I didn't get ur question, is you want a "vertical deravite" then it has to be undefined... – Mehul Dec 11 '20 at 07:27
Point taken, maybe the only way to get a vertical slope is to have an undefined slope... – Christina Daniel Dec 11 '20 at 07:28
Hmm is there any other way, I'm just curious if you know pl tell me – Mehul Dec 11 '20 at 07:29
I don't think there is. Slope is defined as rise/run. – Christina Daniel Dec 11 '20 at 07:35

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