Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.
A) and ; saddle point: ; relative maximum value:
B) and ; relative minimum: ; relative maximum value:
C) and ; saddle point: ; relative minimum value:
D) there are no critical points

Question

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function. ​  ​
A) and ; saddle point: ; relative maximum value: ​ 
B) and ; relative minimum: ; relative maximum value: 
C) and ; saddle point: ; relative minimum value: ​ 
D) there are no critical points

Quizplus · Accepted Answer

To find the critical points, we need to find the points where the first derivative is zero or undefined. Here, no function is given, so we cannot find the first derivative. Therefore, there are no critical points, except if the function is a constant, in which case every point is a critical point. However, we cannot determine the nature of these critical points or relative extrema without knowledge of the original function.

Find the Critical Point(s) of the Function