009A Sample Midterm 2, Problem 2

From Math Wiki
Revision as of 19:33, 13 April 2017 by MathAdmin (talk | contribs)
Jump to navigation Jump to search

The function    is a polynomial and therefore continuous everywhere.

(a) State the Intermediate Value Theorem.

(b) Use the Intermediate Value Theorem to show that    has a zero in the interval  

What is a zero of the function  
        A zero is a value    such that  


Intermediate Value Theorem
        If    is continuous on a closed interval  
        and    is any number between    and  

        then there is at least one number    in the closed interval such that  


Step 1:  
First,    is continuous on the interval    since    is continuous everywhere.




Step 2:  
Since    is between    and  
the Intermediate Value Theorem tells us that there is at least one number  
such that  
This means that    has a zero in the interval  

Final Answer:  
    (a)     See solution above.
    (b)     See solution above.

Return to Sample Exam