2023 AP Calcululs AB & BC FRQ #4
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- Опубликовано: 11 сен 2024
- 2023 AP Calculus AB & AP Calculus BC Exam Free Response Question #4
Function Analysis (Working with the first derivative)
Topics: max/min/neither; intervals concave down from f’; limit; l’hopital’s rule (l’hospital’s rule); absolute minimum (candidates test)
See more about L’Hospital’s Rule on the AP Exam here: • Using L'Hopital's Rule...
Just wanna say thank you as I used your videos a lot to study before the exam. Definitely wouldn’t have done well without you
Awesome! Congrats on finishing the exam.
Thanks so much for your help, I cant express how much your AP review quizes, rate in rate out video and your FRQ videos for each year helped. Thank you!!
happy to hear some of my stuff was helpful! please share with your teacher/friends, in case future people can benefit too!
I do have a quick question tho. Regarding part a what I wrote is "Neither; because when x < 6, f'(x) >0 and when x > 6, f'(x) is also greater than 0". Would this be considered correct?
I don't think so, heres the scoring guide from the official website on this question
•A response that declares f ′( x) does not change sign at x = 6, so neither, is sufficient to earn
the point.
• A response does not have to present intervals on which f ′( x) is positive or negative, but if any are
given, they must be correct. Any presented intervals may include none, one, or both endpoints.
• A response that declares f x ′( ) > 0 before and after x = 6 does not earn the point.
all i did for part c was L’Hopital’s rule then found the limit, i hope that was enough 😭 4:02
remains to be seen on the scoring guidelines. you'll get the vast majority of the points at minimum, maybe all of them (we can hope!)
For 2b would saying f is concave down on (-2,0) and (4,6) because f’’(x)
I’m not clear on what the ruling is on that. Generally you have to connect the explanation to the given. So f” is negative “because f’ is decreasing. “
One of my students asked if it’s okay to justify that there is a point of inflection at x=6 so therefore it’s neither a relative max nor a relative min. Unusual approach but it sounds like as long as they properly explain the reasoning it should work.
That’s a really interesting response. I think it definitely gets the point.
Turk I have a question please , there is a question that says find the volume of s which has the equation y=e of x -2 (-2down) but using rectangle cross section with height 5 times base , since region s is under the x axis well the answer be the integral from 0 to ln 2 of(0)-(e^x -2)^2 times 5 dx?
Or without the 0 minus the whole equation? Please I need answer
Is it correct?
Based on the frqs compared to last year... how do you think the curve is going to compare to last years?
i really think it'll be about the same. it never moves all that much.
Is the candidates test necessary to solve part d? Like could you just say that since f'(x) goes from negative to positive as it crosses x=2 then x=2 would have to be a minimum?
You don't have to use the candidates test, but you do have to address that the question is about an absolute minimum, not a relative minimum. So you have to account for the end points somehow or make clear that they yield larger values. Good question!
At least I know I got at least 7/9 on this FRQ
Is it okay to say "As f'(x) > 0 for 2 < x < 8, both f(6) and f(8) are greater than f(2), and thus can't be the absolute minimum"?
yeah, not just okay, almost certainly better. candidates test was kind of annoying on that one!
thats what i said too
Could you do the international FRQ?
I would if they released them but unfortunately they only put out one set per year!
wait does it matter if we wrote it as (-2,0) and (4,6) on part b 1:42
like...did you mention they were intervals somehow? otherwise they kind of look like ordered pairs. not sure how they score that. (sometimes they're lenient, sometimes they're crazy strict on fine details.)
You should earn the point since it’s interval notation. I did the same as well. The readers will know what you meant even if you didn’t do inequality notation.
thank you for clutching us for the ap exams dude
I'm trying to get everyone a 5 on this thing!
For some reason I said -1
it happens. testing situations are very different from casual study/review.