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Math Help - finding the first and second derivative of a peicewise function

  1. #1
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    finding the first and second derivative of a peicewise function

    i need help finding the first and second derivative of this peicewise function

    f(x)= { 2(x+1)^2 , x<1
    { -x^2 +9 , x >= 1


    the two { are supposed to be one big {

    oh and when you want to check for concavity and increasing and decreasing, do you check each function of the peicewise seperately?

    thanks in advance
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  2. #2
    Senior Member Shanks's Avatar
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    f'(x)=4(x+1),f''(x)=4 \text{ if }x<1;<br />
f'(x)=-2x,f''(x)=-2 \text{ if }x>1
    the first and second derivative of f(x) at the point x=1 don't exist!
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  3. #3
    Newbie drop10's Avatar
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    The important part to remember about integrating or differentiating piecewise functions is that you have to treat them in separate pieces, with the connecting values generally being discontinuous or non-differentiable.
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