The graph of shown below consists of three line segments and one semicircle.Let .Which of the following statements must be false?
A)
B)
C)
D) has a relative maximum at

Question

The graph of  ​ shown below consists of three line segments and one semicircle.Let  .Which of the following statements must be false? ​  ​
A)​ 
B)​ 
C)​ 
D)​ has a relative maximum at

Quizplus · Accepted Answer

The relative maximum of a function occurs at a point where the slope changes from positive to negative. Looking at the graph, we can see that the slope of the function is positive to the left of the point (5,4) and negative to the right of it. Therefore, (5,4) is a relative maximum point. Therefore, statement D is true and not false. 
Statements A and B are true because the function is continuous and defined at x = -1 and x = 8. Statement C is true because the function is decreasing from x = 3 to x = 8.

The Graph of ​ Shown Below Consists of Three

The Graph of Shown Below Consists of Three