Results 1 to 2 of 2

Math Help - Continuity and Differentiability

  1. #1
    Member
    Joined
    Sep 2009
    From
    Ontario
    Posts
    162

    Continuity and Differentiability

    Okay can somebody please check my answer to this

    The function f is continuous for [-2,1] and differentiable for (-2,1). If f(-2)=-5 and f(1)=4, which of the following statements could be false?
    A) There exists c, where [-2,1], such that f(c)=0
    B) There exists c, where (-2,1) such that f '(c)=0
    C) There exists c where (-2,1) such that f(c)=3
    D) there exists c where (-2,1) such that f '(c)=3
    E) there exists c where (-2,1) such that f(c) is greater than or equal to f(x) for all x on the closed interval [-2,1]

    I don't think that it is A or C because f(-2)=-5 and f(1)=4 so that means that there must be some values in between -2 and 1 that equal 0 and 3 since f is continuous right?

    I know that it is not D because I used the mean value theorem and found that f '(c)=3

    I don't think that it is E because it is a closed interval meaning that there is a max in [-2,1]

    So i think that it is B because although there must be a max and min in [-2,1], they could be on the endpoints since it is a closed interval. The derivative of an endpoint wouldn't be 0

    Is this right? Please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    69
    Yeah, that sounds right. For example, the function may just be a straight line between (-2,-5) and (1,4), in which case f'(x) = 3 for all x in (-2,1). For such a function, b is definitely false.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity and Differentiability
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 10th 2010, 02:32 AM
  2. differentiability and continuity
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 23rd 2010, 07:18 AM
  3. Differentiability and continuity
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 30th 2010, 04:26 AM
  4. continuity and differentiability
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 2nd 2009, 01:03 AM
  5. Continuity/Differentiability
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 2nd 2007, 04:33 PM

Search Tags


/mathhelpforum @mathhelpforum