I'm reading about lateral derivatives...(adsbygoogle = window.adsbygoogle || []).push({});

I know that a function is said derivable on a point if the lateral derivative coming from left and the lateral derivative coming from right are both equal at that point. f'(a) exists only if both f'+(a) and f'-(a) exists and are equal... right?

Ok, now the book shows an example of a function that is not derivable at a point (so it has a "break" in its graph)... so the lateral derivative coming from the left at that point is different from the lateral derivative coming from the right... the book also says that for this function, at this point, there are two possible tangent lines...

My question is: if the lateral derivatives at a point of a function are different, does that implies that there will be two possible tangent lines? ALWAYS? Does this have a proof? Can someone show me the proof?

Thank you

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# Question about derivatives

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