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Math Help - Derivative of piecewise functions...halp!

  1. #1
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    Derivative of piecewise functions...halp!

    So the problem goes like this:

    Let f(x) be -x^3 at x<0 and x^3 at x>=0.

    I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.

    Yes...my teacher is a sadist
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  2. #2
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    Smile

    Quote Originally Posted by deth2munkies View Post
    So the problem goes like this:

    Let f(x) be -x^3 at x<0 and x^3 at x>=0.

    I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.

    Yes...my teacher is a sadist
    I'm a little confused by what you mean by "both the points which they are undefined". As you have written it this function is defined everywhere, and so are the derivatives.

    To take derivatives of piecewise functions you take the derivative of each piece and keep the bounds on x the same.

    For instance,
    if f(x) = 2x for x<0 and f(x)=x^2 for x>=0 then
    the first derivative will be
    f'(x)=2 for x<0 and f'(x)=2x for x>=0.

    Hope this helps with your problem!
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  3. #3
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    Quote Originally Posted by ziggychick View Post
    I'm a little confused by what you mean by "both the points which they are undefined". As you have written it this function is defined everywhere, and so are the derivatives.

    To take derivatives of piecewise functions you take the derivative of each piece and keep the bounds on x the same.

    For instance,
    if f(x) = 2x for x<0 and f(x)=x^2 for x>=0 then
    the first derivative will be
    f'(x)=2 for x<0 and f'(x)=2x for x>=0.

    Hope this helps with your problem!
    Alright, thanks.

    I was only supposed to find the points where the third derivative was undefined, although I realize I didn't word it the best way.
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