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Simple Calculus question but I don't understand

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data

    f(x)= {x^3 - 2x, x<=2
    x + 2, x> 2

    find f'(2)


    2. Relevant equations
    Ok, i tried by taking the derivative of the top equation, since it includes 2, but I got the answer to be 10.


    3. The attempt at a solution

    By book says the answer is undefined, but I dont understand why. Thsi is under "quick review" so I'm thinking I'm making it a lot harder than it should be. Am I missing something? Why is it undefined? I keep getting 10.
     
  2. jcsd
  3. Nov 29, 2011 #2

    Dick

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    Remember the definition of derivative. f'(2) is the limit as h->0 (f(2+h)-f(2))/h. If h is negative and approaching zero, then sure, you get 10. But what about if h is positive and approaching zero?
     
  4. Nov 29, 2011 #3
    ohh. it would equal 1, so 10 doesnt equal 1 so it would be undefined.
     
  5. Nov 29, 2011 #4

    Dick

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    That's it.
     
  6. Nov 29, 2011 #5
    Thanks!
     
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