Why every point of a function where differentiation exists has only one tangent? Can anyone help me out?
Why every point of a function where differentiation exists has only one tangent?
I know the slope at any point of any function is defined by differentiation at that point.But there may be another straight line which touches the function at that point but slope is different from the differentiation value at that point. But this does not happen(I am not considering singular point).

But you have to consider the tangent of a singular point. The tangent only touches a specific singular point and does not touch the neighbour points. There is only a unique tangent which meets this condition. The picture below shows that only one straight line can touch the red point without touching one of the blue points. Any other straight line would touch or intersect one of the neighbour points. With some effort one can imagine this situation for infinitesimally small points.

