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Critical Point Question

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Find any critical point of the following function.

    f(t)= 3 — lt-3l, [-1,5]
    The answer says it has a critical point where t=3.

    2. Relevant equations



    3. The attempt at a solution
    f(t)=3 — lt-3l

    f(t)=3-t+3, t≥3 f'(t)= -1

    f(t)=3-(-t+3), t<3 f'(t) = 1

    The function is not differentiable. And it has no critical point. Two cases have different values -> my answer

    I remember the definition of critical point is where the derivative of the function either is zero or doesn't exist.

    What did I do wrong? and Why is t=3 a critical point?
    Thanks.

     
  2. jcsd
  3. Jan 15, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes, the function is not differentiable at t=3. As you said. Isn't that the same thing as 'derivative doesn't exist' in the definition of critical point?
     
  4. Jan 15, 2012 #3
    oh my. It's right in front of my eyes. I was so locked in on f(t)'= -1 and f(t)'= 1.
    Thank you.
     
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