Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point , if .
A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information

Question

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function  at the critical point  , if  .
A) relative maximum 
B) relative minimum 
C) saddle point 
D) insufficient information

Quizplus · Accepted Answer

The critical point can be classified as a saddle point since the second derivative test yields both positive and negative values. This means that the function changes concavity at the critical point and does not have a local maximum or minimum.

Determine Whether There Is a Relative Maximum, a Relative Minimum