Test- a 78.pdf - Examples 4.31(i Consider the polynomial...

This preview shows page 1 - 3 out of 3 pages.

Examples 4.31. (i) Consider the polynomial function f : R R defined by f(x)=x 4 8x 3 +22x 2 24x+7. Then f is differentiable, and one can easily check that f (x) = 4x 3 24x 2 +44x 24 = 4(x 1)(x 2)(x 3). Therefore, f (x) 0 if x 3 or 1 x 2, whereas f (x) 0 if x 1 or 2 x 3. Thus, f is monotonically increasing on [1, 2] and on [3, ), whereas f is
Image of page 1

Subscribe to view the full document.

monotonically decreasing on [2, 3] and on ( −∞ , 1]. In fact, since f vanishes only at x = 1, 2, and 3, we see that f is strictly increasing on (1,2) and on (3, ), whereas f is strictly decreasing on (2,3) and on ( −∞ ,1). Notice that in an
Image of page 2
Image of page 3
  • Spring '14
  • ThomasW.Appelquist
  • Monotonic function, Convex function, polynomial function

{[ 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