1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find interval

  1. Nov 30, 2005 #1
    Hello
    How do I do the following
    Find the interval on which the curve
    [tex]y = \int_x^0 \frac{1}{1 + t + t^2} dt[/tex]
    is concave upward.

    any help would be great.

    P

    Just in case Latex does not show up
    x
    Large S 1/1(1 + t + t^2) dt
    0
     
  2. jcsd
  3. Nov 30, 2005 #2

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    When, in general, is some function f concave upwards?
     
  4. Nov 30, 2005 #3
    I belive a function f should be concave upward when f''(c) > 0. Am I correct. Don't have my text book on me.
     
  5. Nov 30, 2005 #4

    BobG

    User Avatar
    Science Advisor
    Homework Helper

    Correct.

    Now, if the function f (t) is [tex]y = \int_x^0 \frac{1}{1 + t + t^2} dt[/tex], then what's f'(t). (This is very easy).

    Finding f''(t) is a little harder. Once found set it up as an inequality and solve.
     
  6. Nov 30, 2005 #5
    f' is (x)[tex]y = \int_x^0 \frac{-1-2t}{(1 + t + t^2)^2}[/tex]

    f'' would then be
    [tex]y = \int_x^0 \frac{-1 + 2t + 2t^2}{(1 + t + t^2)^4} dt[/tex]

    is this correct??

    How do I solve an inequality that is this complex(it is complex to me)?? I am really not sure about this.
     
  7. Nov 30, 2005 #6

    BobG

    User Avatar
    Science Advisor
    Homework Helper

    The integral is also called the anti-derivative, so the derivative of [tex]y = \int_x^0 \frac{1}{1 + t + t^2} dt[/tex]
    is just:
    [tex]f'(t)= \frac{1}{1 + t + t^2} [/tex]

    So your second derivative is just:
    [tex]f''(t) =\frac{-1-2t}{(1 + t + t^2)^2}[/tex]
     
  8. Nov 30, 2005 #7

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    Not quite BobG, think about where the x is and what your actually differentiating.
     
  9. Nov 30, 2005 #8
    anybody with some guidence?
     
  10. Nov 30, 2005 #9

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    Erm, you've been given loads and loads, what have you done with what you have been given?
     
  11. Nov 30, 2005 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "Fundamental Theorem of Calculus"!!!


    What is the derivative of [tex]\int_a^x f(t)dt[/tex] according to the Fundamenta Theorem of Calculus? (This is what Bobg was doing.)

    Knowing that, what is the derivative of [tex]\int_x^a f(t)dt[/tex]? (This is what Bobg should have done!)


    What is the derivative of [tex]\int_x^a f(t)dt[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Find interval
  1. Find interval of X (Replies: 2)

Loading...