Very obscure/confusing question on quiz today

1. Oct 21, 2011

Frosteh

1. The problem statement, all variables and given/known data
This is exactly how this was written on the quiz today:

If f(1)=1 and f'(x)=(1/3) when x=1, find d/dx[f(2x2-x)].

2. Relevant equations

Basic derivative rules (i.e., power rule).

3. The attempt at a solution

The first statement simply determines that f(2x2-x) is true. When taking the derivative of f(2x2-x), you get 4x-1. However, f'(1)=(1/3). When 1 is entered into 4x-1, (1/3) is clearly not the answer. I listed my answer as 12x-3, by setting 4x-1=(1/3), but I'm not sure if this is correct.

Is my professor insane or is this just a trickily worded question?

2. Oct 21, 2011

SteamKing

Staff Emeritus
What happens if you take the derivative of f(2x^2-x) with respect to x? (Don't worry about substituting the values f(1) and f'(1) at this stage.

3. Oct 21, 2011

verty

This is a moderately tricky but well-phrased question. But I think perhaps you do not understand it?

4. Oct 21, 2011

Staff: Mentor

No, not at all. A function value is not something that is true or false.
No, that is incorrect, as pointed out by SteamKing in another post. You need to use the chain rule to evaluate d/dx( f(2x2 - x)).

5. Oct 22, 2011

verty

Mark44 is of course correct, but enough is known in this question not to require doing that.

6. Oct 22, 2011

HallsofIvy

Staff Emeritus
??? How can you possibly evaluate d/dx(f(2x^2- x) without using the chain rule?

7. Oct 22, 2011

verty

There is ambiguity in how one uses language, necessary ambiguity I think, that one cannot avoid. One must be charitable (see Quine, Indeterminacy of translation) when interpreting the words of others.

And on forums this is a bigger problem, of course. I hope what I intended is clear, that one has quite detailed knowledge of f(x).