Interesting tangents problems

Question

My question is simple. I'm teaching Calculus 1 and I'm looking for counterintuitive problems to find tangents. I want to show to my students the importance of the limit definition of tangents.

Thanks

EDIT (Clarification)

I'm looking for tangents which may mislead students. The students think the tangent is a line $A$, but in fact the tangent is another line $B$.

You should elaborate on what you mean by counter-intuitive problems. — najayaz, Sep 22 '15 at 17:26
@G-man I'm looking for tangents which may mislead students. The students think the tangent is a line $A$, but in fact the tangent is another line $B$. — user42912, Sep 22 '15 at 21:45

score 0 · Answer 1 · answered Sep 23 '15 at 08:42

0

Consider the following function $f(x)$ $$ \begin{array}{ll} 1-x^2 & x\neq0\\ 2 & x=0 \end{array} $$ Looking at the graph one might think that at the point $x=0$, the tangent is $y-1=0$, but in fact by limit definition it should be the Y-axis.

Is this the kind of thing you were looking for?

answered Sep 23 '15 at 08:42

najayaz

5,459

Thank you for your answer. It's exactly I was looking for! – user42912 Sep 24 '15 at 12:11
The function is not derivable at this point, can I say there is a tangent at $x=0$? – user42912 Sep 24 '15 at 12:12
@user42912 Geometrically speaking I think the tangent should exist but calculus will disagree. – najayaz Sep 24 '15 at 15:17

Interesting tangents problems

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