1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted