Question

If f(x) = 3a|2x – 4| – ax, where a is some constant, find f ′(2).

Answer 1

What class is this for?

Answer 2

ap calc ab

Answer 3

OK, that makes sense. I'm thinking... :)

Answer 4

answer choices:
not enough information
1
0
DNE

Answer 5

DNE what's this

Answer 6

does not exist

Answer 7

what do u think?

Answer 8

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.

Answer 9

What, if I say the function doesn't exist if it has a =0.

Answer 10

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.

Answer 11

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.

Answer 12

I'm not sure I'm seeing your point... But, please explain. :)

Answer 13

Are you suggesting that a must equal 0, otherwise f'(2) can't be found?

Answer 14

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.

Answer 15

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. :)