According to Mean-Value Theorem (MVT) in Calculus, "There is a point $c$, such that $a < c < b$, at which the tangent line is parallel to the secant line through $(a,y(a))$ and $(a, y(b))$". I have these 2 graphs and which do not conform to MVT. I have my reasons here why they do not, I want to know if I am correct.
Red lines are $Secant-Lines$. It can be easily seen that graph-1 has asymptotic discontinuity and graph-2 has jump discontinuity. Secant lines are red and there can be drawn not one tangent line that is parallel to the secant line in both graphs. Hence, MVT is not applicable .