Consider the contour graph and the three-dimensional graph for the function R, given below. What critical point is represented by the point A on the contour map?
A) relative maximum
B) saddle point
C) global maximum
D) relative minimum
E) not a critical point

Question

Consider the contour graph and the three-dimensional graph for the function R, given below. What critical point is represented by the point A on the contour map?  
A) relative maximum 
B) saddle point 
C) global maximum 
D) relative minimum 
E) not a critical point

Quizplus · Accepted Answer

Point A is where two contour lines intersect, indicating that it is a critical point. Additionally, the contour lines on either side of point A are increasing in one direction and decreasing in the other, which is characteristic of a saddle point in the three-dimensional graph. Therefore, the best choice is B, saddle point.

Consider the Contour Graph and the Three-Dimensional Graph for the Function