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!

True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equals c

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equals c


    2. Relevant equations



    3. The attempt at a solution
    I know that if f'(a) exists the statement is true, but is it true that based on that information f'(a) exists?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 27, 2013 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

    Look at the definition of the derivative. [itex]f'(a) = c[/itex] means that
    $$\lim_{x \rightarrow a}\frac{f(x) - f(a)}{x - a} = c$$
    Try applying the mean value theorem to
    $$\frac{f(x) - f(a)}{x - a}$$
    and see if you can conclude anything.
     
  4. Jan 27, 2013 #3
    Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

    yes, my teacher explained t that way but the last part of the demonstracion when he uses some theorem about the limit of compound functions with csi(x) is really confusing..
     
  5. Jan 27, 2013 #4

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equa

    Suppose [itex]x > a[/itex]. Does the mean value theorem apply to [itex]f[/itex] on the interval [itex][a, x][/itex]? If so, what does it say?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: True/False:f(x) is continous, limit of f'(x) as x->a is c, then f'(a) EXISTS equals c
Loading...