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Math Help - Is y= x^2-|x-4| differentiable at x=4?

  1. #1
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    Is y= x^2-|x-4| differentiable at x=4?

    Doesn't x^2 mean it'll be a parabola and thus differentiable for all x? That's what I thought but the absolutes screw me up
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  2. #2
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    Quote Originally Posted by -DQ- View Post
    Doesn't x^2 mean it'll be a parabola and thus differentiable for all x? That's what I thought but the absolutes screw me up
    I guess you could follow this procedure:

    for x > 4:
    <br />
y=x^2 - x +4<br />
    and its derivative is: 2x-1

    for x<4:
    <br />
y=x^2+x-4<br />
    and its derivative is: 2x+1

    lim(2x-1) for x approaches to 4+ is 7;
    lim(2x+1) for x approaches to 4- is 9;

    so y's derivative is not continuous at x=4, thus y is not differentiable at x=4.

    may this help you.
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  3. #3
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    cool. it's weird because the graph looks like it doesn't but it does when you prove it like that.
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