The figures show a contour graph for a function f in blue with a constraint function in black. Locate any optimal points of and classify each as a relative maximum point or a relative minimum point.
A) (31, 10, 4)
B) (32, 14, 2)
C) (35, 16, 2)
D) (32, 16, 2)
E) (35, 18, 2)

Question

The figures show a contour graph for a function f in blue with a constraint function  in black. Locate any optimal points of  and classify each as a relative maximum point or a relative minimum point. 
A) (31, 10, 4) 
B) (32, 14, 2) 
C) (35, 16, 2) 
D) (32, 16, 2) 
E) (35, 18, 2)

Quizplus · Accepted Answer

From the contour graph, we can see that the optimal points must lie on the constraint curve. By comparing the heights at the given points, it can be seen that point C (35,16) has the highest value for the function f, while all other options have lower values. Therefore, C must be the relative maximum point.

The Figures Show a Contour Graph for a Function F