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Calculus Problem, Estimate h'(-1)

  1. Aug 28, 2010 #1
    1. The problem statement, all variables and given/known data
    A function f with domain [-5, 5] has a derivative f' whose graph is shown http://img718.imageshack.us/img718/2842/calcpic.jpg" [Broken]. Also, f(-1) = 2.

    a) If h(x) = ef(x), estimate h'(-1).


    2. The attempt at a solution

    a)
    h'(x) = f'(x)ef(x)
    h'(-1) = f'(-1)ef(-1)
    = e2f'(-1)

    f'(-1) = (2 - 3)/(0-(-1)) = -1/1 = -1

    h'(-1) = -e2

    Issues I'm having

    So I'm not exactly sure if my estimate of f'(-1) is accurate based on the graph. What do you all think?

    Thanks,
    Bob :)
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 28, 2010 #2

    lanedance

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    doesn't f'(-1) = 3 from that picture?
     
  4. Aug 28, 2010 #3
    Hahaha, oh my gosh I'm stupid. Thank you. :P
     
  5. Aug 28, 2010 #4
    Another part of the question is:

    Suppose that g(x) = 1/[f(x)]2. Is g(x) increasing when x = -1? Explain.

    It would be decreasing, right? Because the derivative is -1/4. I don't get how to explain that...
     
  6. Aug 28, 2010 #5

    lanedance

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    so if you caclulate the derivtive of g(x) is negative, then that is sufficient to explain it is decreasing
     
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