Results 1 to 2 of 2

Math Help - Differential Calculus

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Canada
    Posts
    5

    Differential Calculus

    The problem reads like this:

    Is it possible for a continuous smooth function g(x) on the domain [-6, 6] to have an absolute maximum at a point x0 in [-6, 6] without the derivative f'(x0) being 0? If so, draw an example of such a function.

    Here are my workings:
    I think that it is not posible to have absolute maximum without being f'(x0) = 0. Am I correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Re: Differential Calculus

    How about considering a monotonic increasing function such as f(x)=x^3 over the domain? Notice that f(x) is maximized when x_0 = 6 , but  f'(6)=2(6)^2 \neq 0 . The key here is that the absolute maximum can exist on the boundary in this case, but if the domain is  (-6,6) then it won't happen.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differential Calculus
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 19th 2009, 08:44 AM
  2. Differential Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 14th 2009, 06:44 PM
  3. Differential calculus?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 30th 2008, 09:58 AM
  4. Differential calculus
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 29th 2008, 04:10 AM
  5. differential calculus
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 16th 2008, 03:54 PM

Search Tags


/mathhelpforum @mathhelpforum