Results 1 to 2 of 2

Math Help - Calculas Problem, difficult

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    95

    Calculas Problem, difficult

    Let f(x) be a function that is continuous on the interval [-10, 10], has continuous first and second derivatives on (-10, 10), and has values f(-10)=4, f(0)=-2, and f(10)=8.

    a) Show that there is a point a in (-10, 10) such that f'(a)<0

    b) Show that there is a point b in (0, 10) such that f'(b)>0

    c) Using the results from parts a & b, must f have a critical number in (-10, 10? Explain why f must have a critical number or give an example of a function that satisfies the criteria but has no critical number.

    Very difficult, please help. ( *bows to math people*
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,894
    Thanks
    326
    Awards
    1
    Quote Originally Posted by Hibijibi View Post
    Let f(x) be a function that is continuous on the interval [-10, 10], has continuous first and second derivatives on (-10, 10), and has values f(-10)=4, f(0)=-2, and f(10)=8.

    a) Show that there is a point a in (-10, 10) such that f'(a)<0

    b) Show that there is a point b in (0, 10) such that f'(b)>0

    c) Using the results from parts a & b, must f have a critical number in (-10, 10? Explain why f must have a critical number or give an example of a function that satisfies the criteria but has no critical number.

    Very difficult, please help. ( *bows to math people*
    a) f(-10) = 4 and f(0) = -2. What is the criterion for a function to be decreasing?

    b) f(0) = -2 and f(10) = 8. What is the criterion for a function to be increasing?

    c) Somewhere on (-10, 0) the function has a negative derivative and somwhere on (0, 10) the function has a positive derivative. Can we say there is someplace where the derivative is 0? (Remember that the function and its first and second derivatives are continuous.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Calculas of Variations problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 29th 2009, 01:43 AM
  2. calculas problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 24th 2008, 08:38 PM
  3. Small problem with calculas
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 25th 2008, 10:15 PM
  4. Help Calculas
    Posted in the Calculus Forum
    Replies: 19
    Last Post: October 24th 2008, 07:32 PM
  5. Calculas Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2008, 11:23 PM

Search Tags


/mathhelpforum @mathhelpforum