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Use the definition of the derivative to determine all possoble values of A and B?

  1. Sep 27, 2008 #1
    Use the definition of the derivative to determine all possoble values of A and B?
    Use the definition of the derivative to determine all possoble values of A and B that make the function f differentiable at 0.


    F(x)={ Ax^2 + Bx if -infin < x <= 0
    { x^3/2*cos(1/x) if 0<x<infin

    I used defintion of derivative and equated both sides after i got both derivatives but i cant solve for the constants

    any help
     
  2. jcsd
  3. Sep 27, 2008 #2

    lurflurf

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    A and B need to be chosen so that
    f(0-)=f(0)=f(0+)
    f'(0-)=f'(0)=f'(0+)
    what do you find for
    f(0-)
    f(0)
    f(0+)
    f'(0-)
    f'(0)
    f'(0+)
    ?
     
  4. Sep 27, 2008 #3

    lurflurf

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    especially f'(0+)
    are you sure the question is as written?
     
  5. Sep 28, 2008 #4
    yea the questoin is written correctly. This is part a: use differentiation formulas to find a formula for f''(x) for -infin<x<0 and 0<x<infin

    and part b is the one i posted
     
  6. Sep 28, 2008 #5

    arildno

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    " x^3/2*cos(1/x) if 0<x<infin"
    I presume this should be read as:
    [tex]x^{\frac{3}{2}}\cos(\frac{1}{x}), 0<x<\infty[/tex]?

    Take care to use the proper definition of the derivative at x=0..
     
    Last edited: Sep 28, 2008
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