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OK. I have a Calc Multiple Choice Problem, but it looks like 2 answers are right?

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Multiple Choice If f is a continuous, decreasing function on
    [0, 10] with a critical point at (4, 2), which of the following statements
    must be false? E
    (A) f (10) is an absolute minimum of f on [0, 10].
    (B) f (4) is neither a relative maximum nor a relative minimum.
    (C) f ' (4) does not exist.
    (D) f ' (4) = 0
    (E) f ' (4) < 0



    2. Relevant equations

    Ok. It looks to me like C and E are both false, based on the mere fact that D is correct, making this question have 2 answers.
    Can someone please explain to me why one of them should be incorrect?


    3. The attempt at a solution

    Thanks in advance!
     
  2. jcsd
  3. Nov 30, 2011 #2

    micromass

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    How did you define critical point??
     
  4. Nov 30, 2011 #3
    critical point was where f '(x)= 0, so i said f '(4)=0
     
  5. Nov 30, 2011 #4

    micromass

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    Under that definition, it seems indeed true that C and E are false. However, I would doublecheck that definition if I were you.
     
    Last edited: Nov 30, 2011
  6. Nov 30, 2011 #5

    Ray Vickson

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    No. A function can be *strictly decreasing* and yet have a critical point. For example, [itex] f(x) = -x^3[/itex] is strictly decreasing but has [itex] f'(0) = 0 [/itex]. (It is strictly decreasing because for any [itex] x_1 < x_2[/itex] we have [itex] f(x_1) > f(x_2).[/itex])

    RGV
     
  7. Nov 30, 2011 #6

    Mark44

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    Yeah, critical points aren't just where the derivative is zero...
     
  8. Nov 30, 2011 #7

    micromass

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    Yes, how does that contradict what I said??
     
  9. Nov 30, 2011 #8

    Ray Vickson

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    Sorry: it doesn't; I did not read the questions A--E carefully enough.

    RGV
     
  10. Nov 30, 2011 #9
    Ok, so the answer is E then.
    Thanks!
     
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