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Find the Values for which the function is continuous

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine the values of k,L,m and n such that the following function g(x) is continuous and differentiable at all points

    2. Relevant equations

    2x2-n if x<-2
    mx+L if -2≤x<2
    kx2+1 if x≥2


    3. The attempt at a solution

    So I know that for the function to be continuous the limit as x→c of f(x) must equal f(c)
    And I am trying to make this function continuous for all values of k,L,m and n.

    so I done the following
    2x2-n = mx+L for x=-2
    mx+L = kx2+1 for x= 2

    and I simplified them to the following.
    2m-n+5=0
    2m-4k+L=0


    From here I don't know what to do... I'm pretty sure that I am correct up to here but could someone just please tell me what to do now...
    I don't know how to solve for 4 variables with only 2 equations
     
  2. jcsd
  3. Apr 29, 2012 #2
    just differentiate and then equate them to find.four eqn four unknown
     
  4. Apr 29, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You should know that all polynomials are both continuous and differentiable for all x so that only points in question are x= -2 and x= 2


    What happened to the "L"? At x= -2, the first equation becomes
    2(-2)2- n= m(-2)+ L which simplifies to 8- n= -2m+ L or 2m- n+ 8- L= 0.

    And here, what happened to the "1"? At x= 2, the second equation becomes m(2)+ L= k(4)+ 1 or 2m- 4+ L- 1= 0

    You have not yet said any thing about being "differentiable".

    (Note, the derivative of a function is NOT necessarily differentiable but it does satisfy the "intermediate value property" so IF the limit from each side exist, then they must be equal.)
     
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