MA113_S13_Assignment4_solutions

MA113_S13_Assignment4_solutions - MA 113 Calculus I Spring...

Info icon This preview shows pages 1–2. Sign up to view the full content.

MA 113 – Calculus I – Spring 2013 Written Assignment #4 Due Friday, March 1, 2013, at beginning of lecture Question A: Figure (A) shows f and figure (B) shows f ′′ . Sketch the graph of f and explain your reasoning. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 (A) (B) Solution: We can see by looking at figure (A) that the graph of f has a horizontal tangent line at x = - 1 and x = - 0 . 25. Then the graph of f will have x -intercepts at x = - 1 and x = - 0 . 25. We also note that f ( x ) is decreasing when x is in interval ( - 1 , - 0 . 25) and f ( x ) is increasing for x in the intervals ( -∞ , - 1) and ( - 0 . 25 , ). Hench the graph of f will be negative for x in the interval ( - 1 , - 0 . 25) and positive when x is in the intervals ( -∞ , - 1) and ( - 0 . 25 , ). Next we examine figure (B). From the graph we see that f ′′ ( - 2 / 3) = 0, thus the derivative of f ( x ) is 0 at x = - 2 / 3. In other words, the graph of f has one horizontal tangent line at x = - 2 / 3.
Image of page 1

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

Image of page 2
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