tmagloire1
  • tmagloire1
If f(x) = 3a|2x – 4| – ax, where a is some constant, find f ′(2).
Mathematics
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SOLVED
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chestercat
  • chestercat
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jtvatsim
  • jtvatsim
What class is this for?
tmagloire1
  • tmagloire1
ap calc ab
jtvatsim
  • jtvatsim
OK, that makes sense. I'm thinking... :)

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More answers

tmagloire1
  • tmagloire1
answer choices: not enough information 1 0 DNE
princeharryyy
  • princeharryyy
DNE what's this
tmagloire1
  • tmagloire1
does not exist
princeharryyy
  • princeharryyy
what do u think?
jtvatsim
  • jtvatsim
EDIT: This one seems a bit strange... If you think about it, there are two possible values of |2x - 4| either (2x - 4) when x >= 2 or -(2x - 4) when x < 2. On one hand, f(x) = 3a(2x - 4) - ax, so f'(x) = 6a - a = 5a, when x>= 2 On the other, f(x) = -3a(2x - 4) - ax, so f'(x) = -6a - a = -7a, when x < 2. If a is not 0, then f'(2) is at a sharp point where the slopes 5a and -7a meet, which means it does not exist. However, if a = 0, then the slopes 5a and -7a are both 0, and f'(2) does exist. The best answer seems to be that there is not enough information. We need to know more about a.
princeharryyy
  • princeharryyy
What, if I say the function doesn't exist if it has a =0.
jtvatsim
  • jtvatsim
Well, the zero function is a perfectly valid function. Set f(x) = 0. This is a true function that for every x returns the value 0.
princeharryyy
  • princeharryyy
yes! that's what I was trying to tell you. You know the logic! great! what could this possibly mean. Do you still think there isn't enough information given to solve the problem.
jtvatsim
  • jtvatsim
I'm not sure I'm seeing your point... But, please explain. :)
jtvatsim
  • jtvatsim
Are you suggesting that a must equal 0, otherwise f'(2) can't be found?
princeharryyy
  • princeharryyy
the exegesis is pretty simple, now that the value can be any integer and the function still stays a function, even when you put a as zero and also the second situation i.e. f'(2) still holds true when a is zero, that means a should be zero.
jtvatsim
  • jtvatsim
OK, I see your point. I think this is a matter of interpretation of the question. The way I am reading it, a is "some constant" that is free to be whatever it wants before we ever even read the question. It is some given. That is why my answer is "not enough information." If we take your point of view, it would seem like a is "yet to be determined" and needs to be found to be something nice and convenient. Then, the answer would be f'(2) = 0. It depends on the author's original formulation. :)

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