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Continuously Differentiable

  1. Dec 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Given the function:
    1, x≤0;
    [itex]\phi[/itex]={1-3x^2+2x^3, 0<x<1;
    0, x≥1.
    Show that [itex]\phi[/itex] is continuously differentiable and provide its equation
    2. Relevant equations

    3. The attempt at a solution
    I have figured out that it is continuously differentiable because the limit as x approaches 0 is 1, and as it approaches 1 it is zero; thus there is no discontinuities. However, what would the derivate equation be? Thanks
  2. jcsd
  3. Dec 9, 2013 #2


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    Science Advisor
    Homework Helper

    hi swhww3! welcome to pf! :smile:
    you've only proved that it is continuous
    the equation for the derivative will be in three parts, like the original equation :wink:
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