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

The statement says that if a point is a critical point for one function and satisfies another function at that point, then the second function cannot have a relative extremum at that point. This is true because if a function has a relative extremum at a point, then its derivative at that point must be zero or undefined. But if the second function satisfies the first function at that point, then their derivatives at that point must be equal, which means the derivative of the second function is also zero or undefined. Therefore, the second function cannot have a relative extremum at that point. Choice B correctly states that 11eb12b0_a92f_10a2_b394_c3dd0bd8e590_TB7866_11 cannot have a relative extremum at 11eb12b0_a92f_37b3_b394_3f8412fe66cb_TB7866_11, which satisfies the condition in the statement.

Determine the Statement Is True or False