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Math Help - Differentiable question

  1. #1
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    Exclamation Differentiable question

    One more question i find myself stuck at. Once again thanks in advance!

    f(x)= { 2kx^2-x , x>3
    x^3 +cx , x <(or equal to) 3

    What is the value of k+c if the function is differentiable everywhere?
    Last edited by painterchica16; September 22nd 2008 at 06:31 PM.
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  2. #2
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    Quote Originally Posted by painterchica16 View Post
    One more question i find myself stuck at. Once again thanks in advance!

    f(x)= { 2kx^2-x , x>3
    x^3 +cx , x <(or equal to) 3

    What is the value of k+c if the function is differentiable everywhere?
    You need a smooth join at x = 3.

    So f(x) is not allowed to have a jump discontinuity and f'(x) is not allowed to have a jump discontinuuity at x = 3.

    So solve the following equations simultaneously:

    2k(3)^2 - 3 = (3)^3 + c(3) .... (1)

    4k(3) - 1 = 3 (3)^2 + c .... (2)
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