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# Difficult AP Calc BC Bonus Questions (trick?)

Registered User Posts: 600 Member
edited November 2007
So here are 2 questions that are connected in some way. In the past 12 years, no one has been able to solve both of them. Both are NOT trick questions, but they seem more difficult than they look.

Let f(x) be continuous and differentiable function for all x.

1. If f(3) = 5, find f'(x) *HINT* No limits are involved in figuring out the solution

2. Differentiate both sides of the equation f(3) = 5

My progress:

1. Well I claimed (-infinity, +infinity) after thinking about the possibilities. The teacher told me I was on the right track but I needed more so I think the solution is more complete or I'm missing something.

2. For the second one, I had (-infinity, +infinity) for the left side and then 0 on the right side. This made no sense to me, the teacher said I was so close yet so far away from the solution.

Any ideas?
Post edited by snipez90 on

## Replies to: Difficult AP Calc BC Bonus Questions (trick?)

• Registered User Posts: 513 Member
First of all, is that all you're given?
• Registered User Posts: 810 Member
Well, f(3) is a constant (since it is equal to 5), and accordingly, d/dx[f(3)] = 0.

I can't imagine that f '(x) is (-infinity, infinity). That seems like the domain of f '(x), and possibly the range of f '(x), but not the function itself.

One key idea that your teacher might be hinting at is the idea that f '(3) and d/dx[f(3)] are not the same thing. The idea is that the first is saying find the derivative of f(x) and evaluate it at x = 3, while the second is saying find the derivative of the constant f(3). But the question as phrased seems to be looking for something more sophisticated than that.

I'm 99% certain that the answer to the second question is therefore 0 = 0.

I'm also 99% certain that you have insufficient information to answer the first question (at least as it is relayed here). Telling you the location on one point on f(x) doesn't give you enough information to say anything about the rate of change of the function. Does f '(x) exist? Sure, and you know that because f(x) is differentiable for all x (which incidentally, makes the remark about f(x) being continuous a redundant remark). Can you determine what f '(x) is? I would venture not. There's no function to take the derivative of. There's no hint as to the type of function that f(x) is. And one point does not a derivative function make.

So unless there is more to the question than what is given, I would say that there is insufficient information to answer the first.
• Registered User Posts: 600 Member
@Gator, yeah that's all the info, exact problem statements:

Given f(x) is continuous and differentiable for all x, if f(3) = 5 then f'(3) =

Given f(x) is continuous and differentiable for all x, differentiate both sides of the following equation: f(3) = 5

@mathprof, it also makes sense to me why the second one would be 0 = 0, since f(3) is constant because its value IS 5. The first question is still a bit baffling.

Anyways, I just thought this set of questions was kind of interesting.
• Registered User Posts: 810 Member
f '(3) is slightly more information than f '(x), but I still don't think there's a solution without having another point or some kind of information about f(x) to assist.

Sorry I couldn't be of more help.
• Registered User Posts: 600 Member
MathProf you were right on the money. I cross checked with a former student. The first case bugs me a little because I can't just say the set of real numbers because it's simply not a suitable answer.

But yeah, let's agree that it's more of a question of semantics rather than calculus.
• Registered User Posts: 1 New Member
GUO CHEN! I consider this Cheating! we are gonna have a chat tomorrow!
• Registered User Posts: 527 Member
plea for the "collaboration"
• Registered User Posts: 426 Member
ahahahhahahaha

the OP just got caught
• Registered User Posts: 90 Junior Member
ROFL dam that must suck to get caught on CC sucks but sure is hilarious
• Registered User Posts: 784 Member
Don't you think it's more likely that a classmate who knows his online alias is just trying to scare the crap out of him, rather than his math teacher stumbling upon this post?

It's possible, just saying...
• Registered User Posts: 810 Member
I would dare say "likely" that it's a classmate.

I don't know many teachers who would start their post Hahahahahahaha
• Registered User Posts: 600 Member
dude, it's DAQUILA not DEQUILA :P
• Registered User Posts: 185 Junior Member