Determine whether 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 false.
If and , then f must have a critical point at (a, b).

A) False. In relative extremum and .
B) True. It follows from definition.

Question

Determine whether 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 false. ​
If  and  , then f must have a critical point at (a, b).
​
A) False. In relative extremum and . 
B) True. It follows from definition.

Quizplus · Accepted Answer

According to the statement, the two given expressions must have a common critical point. This is true according to the definition of a critical point, which is a point where the derivative of the function is either zero or undefined. Therefore, if f has a critical point at (a,b) in one expression, it must also have a critical point at (a,b) in the other expression, since they only differ in one coefficient.

Determine Whether the Statement Is True or False