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Continuous function

  1. Oct 19, 2007 #1
    OKKK,

    f(x) =

    2x + 1, for x =< (greater than or equal to) 2
    .5x^2 + k for x > 2

    ---

    FOR what value of k will f be continuous ?

    MOST IMPORTANTLY, if k=4, is f differentiable at 2?
     
  2. jcsd
  3. Oct 19, 2007 #2
    you're going to have to try a little harder than that
     
  4. Oct 19, 2007 #3
    why would you even respond if youre going to be rude?

    i already did it i just wanted to see what other people got

    at K = 3 it should be continuous and i think at k=4 it will be differentiable because the derivative from the left = 2 and the derivative from the right will be x or in this case 2

    CORRECT? OR NOT?
     
  5. Oct 20, 2007 #4
    continuous for k=3.
    because both functions have the same value @ x=2 and therefore the graph doesn't have a "jump" or a "step". More precisely, the limit @ x=2 (the transition point) is equal to some number.

    for k=4, check at x=2.

    if both equations are not equal then you cannot differentiate at that point.
     
  6. Oct 20, 2007 #5
    i wasn't being rude because you're being ignorant. 1 this isn't the hw forum ,2 we don't do your homework for you, 3 i can't read your mind and know you've already done the problem.
     
  7. Oct 20, 2007 #6
    i am in calculus therefore i am ignorant!
     
  8. Oct 21, 2007 #7
    i really don't think that's the reason he thinks ur ignorant, its cuz u posted HW problems on the NOT-HW forum. THe calculus/analysis forum will tolerate help being asked for problems but generally not of this sort because it is somewhat formulaic. When I ask for help here I detail my solution (and i usually have a complete one at the time of posting). One typically asks for feedback on an idea they might have.
     
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