Very obscure/confusing question on quiz today

[Frosteh]

Homework Statement

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)].

Homework Equations

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

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?

 

[SteamKing]

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.

 

[verty]

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

 

[Mark44]

Homework Statement

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)].

Homework Equations

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

The Attempt at a Solution

The first statement simply determines that f(2x²-x) is true.

No, not at all. A function value is not something that is true or false.

When taking the derivative of f(2x²-x), you get 4x-1.

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)).

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?

 

[verty]

You need to use the chain rule to evaluate d/dx( f(2x2 - x)).

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

 

[HallsofIvy]

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

 

[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).