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: 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?

  2. jcsd
  3. Jan 15, 2012 #2


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