Question

how do you know whether the endpoint of a graph is a critical point ? thanks .

Answer 1

Critical points are defined as being:
1) Endpoints of a graph
2) Where the derivative of the function is equal to zero
3) Where the derivative is undefined.

The concept of critical points are introduced because these are the only points a function can attain its extreme values, whether local or global.

Answer 2

So, to answer your question: You know because it is defined to be