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Math Help - Derivative question

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    Derivative question

    I don't know how to find where the derivative exists or where it fails to exists? and where all the points exists for these functions?
    (btw its suppose to be a big parentheses holds both functions)

    f(x)={ (x-1)^3, x≥1 and x^3-3x+2, x<1 }
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  2. #2
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    Quote Originally Posted by popcandy View Post
    I don't know how to find where the derivative exists or where it fails to exists? and where all the points exists for these functions?
    (btw its suppose to be a big parentheses holds both functions)

    f(x)={ (x-1)^3, x≥1 and x^3-3x+2, x<1 }
    1. show f(x) is continuous at x = 1 using the three-part definition of continuity at a point. then ...

    2. show f(x) is differentiable at x = 1 using the definition of a derivative at a specific point ... you'll need to show

    \displaystyle \lim_{x \to 1^-} \frac{f(x) - f(1)}{x-1} = \lim_{x \to 1^+} \frac{f(x) - f(1)}{x-1}
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