Differentiability and tangent relationship

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(1) We say that if a function at $x=a$ is differentiable, then there exists a tangent.

(2) But if a function have tangent at $x=a$, then it may not be differentiable at $x=a$.

Also, when secants are becoming parallel to each other as $h\rightarrow 0$, the secants approaches to a common tangent at that point. We use this condition to prove that a function is differentiable or not, i.e. LHD=RHD (have a tangent at that point). But in (2) , we have said that it may not be differentiable.

Make it clear to me ASAP.

Thanks in advance.

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An endpoint can have a tangent but is not differentiable because the graph/function is not continuous at the endpoint.