Show that the function has no relative extrema on .
A) The function has no relative extrema by definition of the derivation.
B) The derivation of the function is . At every point the derivative exists and does not equal to 0. So by definition the function has no relative extrema on this interval.
C) The function has no relative extrema because does not equal to 0 at any point.

Question

Show that the function  has no relative extrema on  . ​
A) The function has no relative extrema by definition of the derivation. 
B) The derivation of the function is . At every point the derivative exists and does not equal to 0. So by definition the function has no relative extrema on this interval. 
C) The function has no relative extrema because does not equal to 0 at any point.

Quizplus · Accepted Answer

The best choice is B because it follows from the definition of the derivative that a function has no relative extrema at points where its derivative is nonzero. The statement in choice C is not true, as the fact that the derivative is nonzero does not guarantee that the function has no relative extrema. Choice A is also technically correct but not as precise as choice B.

Show That the Function Has No Relative Extrema on