Determine the statement is true or false. If it is true explain why it is true. If it is false, give an example to show why it is true. If satisfies at a critical point of , then cannot have a relative extremum at .
A) Flase, can have a relative extremum at .
B) True, can not have a relative extremum at .

Question

Determine the statement is true or false. If it is true explain why it is true. If it is false, give an example to show why it is true. If  satisfies  at a critical point  of  , then  cannot have a relative extremum at  .
A) Flase, can have a relative extremum at . 
B) True, can not have a relative extremum at .

Quizplus · Accepted Answer

If a point in a function satisfies the conditions for critical point, then it may or may not be a point of extremum. If a function has a relative extremum at a certain point, it means that the function either has a maximum or a minimum at that point. Since the statement says that a certain point cannot have a relative extremum at another point, it means that the function cannot have a maximum or a minimum at that point. Therefore, the statement is true and the best choice is B.

Determine the Statement Is True or False