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snipez90
Registered User Posts: **600** Member

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?

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

This discussion has been closed.

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

513Member810MemberI 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.

600MemberGiven 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.

810MemberSorry I couldn't be of more help.

600MemberBut yeah, let's agree that it's more of a question of semantics rather than calculus.

1New Member527Member426Memberthe OP just got caught

90Junior Member784MemberIt's possible, just saying...

810MemberI don't know many teachers who would start their post Hahahahahahaha

600Member185Junior Member828Member