275_exam2_solution

# C is it always true that f has an absolute maximum in

This preview shows page 3. Sign up to view the full content.

) there. (c) Is it always true that f has an absolute maximum in (0 , 1)? If yes, prove it, if not then give a counterexample. No. E.g. f ( x ) = x is a function like this and it does not have an absolute maximum in (0 , 1). (Since it’s strictly less than 1 and it can be bigger than 1 - ε for any ε > 0.) 6. Show that the equation x = cos( x 3 ) has at least one real solution. The function f ( x ) = x - cos( x 3 ) is continuous for every x 0 (right-continuous at x = 0). We have f (0) = - 1 and f (4) = 4 - cos(64) 2 - 1 = 1. Thus f (0) < 0 , f (4) > 1 and by Bolzano’s theorem there must be an x (0 , 4) 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern