{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

12.08 - [Hand out cover sheet for exam and read it aloud...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
[Hand out cover sheet for exam and read it aloud] The exam will focus on sections 2.6 to 4.7. You may use a five-page “cheat-sheet”, but it must be created by you; you cannot photocopy reference books or print things out from the web. I aim to arrive here shortly before 11; as soon as everybody’s here, we’ll start the exam. You can stay till 1 p.m. Return HW #10: “There exists a function f such that f ( x ) < 0, f ( x ) < 0, and f ′′ ( x ) > 0 for all x .” ..?.. #10½ (Extra True/False question): Does there exist a twice- differentiable function f on R satisfying f ( x ) < 0 and f ′′ ( x ) > 0 for all x ? ..?.. Use the original definition of concavity. ..?.. Since f ′′ ( x ) > 0 for all x , the function f must be concave up everywhere, so every tangent line to the graph of f must
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
lie completely below the graph of f . And since the graph of f stays below the x -axis, every tangent line to the graph of f must lie completely below the x -axis. Hence … ..?..
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern