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

Option B provides a proper explanation by using the derivative to show that it does not equal to 0 at any point, thus excluding the possibility of relative extrema. Option A simply mentions the definition without any further explanation, and option C incorrectly asserts that the function not being equal to 0 at any point implies the absence of relative extrema.

Show That the Function Has No Relative Extrema on