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. 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.  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

The statement is true because if a function is differentiable at point (a,b), then it must have a critical point at that point since the derivative at that point is zero. This follows from the definition of critical points, which are the points where the derivative is zero or does not exist.

Determine Whether the Statement Is True or False