In a vector valued function ,what does it mean for the derivative to be zero?

In a vector valued function ,if the derivative is zero at a point ,then the function is said to be not continuous at that point,I can't wrap my head around this idea?Could u show via diagram as to how a zero derivative leads to a non differentiable function in the context of vector valued functions.

I don't understand what you mean by "In a vector valued function ,if the derivative is zero at a point ,then the function is said to be not continuous at that point". But if you are talking about functions on real euclidean spaces (ie, $f: E \subset_{\text{open}} R^n \to R^m$) then your statement is wrong. In such functions, differentiability implies continuity. Also when you say the function has zero derivative at some point, then you are explicitly assuming differentiability at that point. So "zero derivative leads to a non differentiable function" is not true either. Here is a example of a vector valued function with a extremal point, having derivative zero.