2024 AP Calculus AB FRQ #5

Free Response Question 5 from the 2024 AP Calculus AB Exam.
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Implicitly defined functions; implicit differentiation. Non-calculator.
tangent line approximation; horizontal tangent lines (slope is 0; derivative is 0); vertical tangent lines (slope is undefined; derivative is undefined); related rates; derivative with respect to t (d/dt).

[@itsmissy_]

i got cooked

[@imnobody101]

I felt good on the MC part of the Exam but then when I started the FRQs I got nervous asf and didnt finish half of two FRQs but seeing these vids makes me feel a bit better bc it looks like I did good on the ones I actually finished

[@jinanren2026]

unfortunately i had the related rates eq correct but calculated wrong but otherwise i mentioned there's not vertical tangent cuz' the slope did not approach infinity... no clue if that works

[@itsdavid5601]

i cooked🔥🔥🔥

[@shabadoey]

same 🔥🔥 we up 💯💯

[@lyonkang7402]

For part b I didn’t use the given dy/dx at all. I just plugged in y=1 to the curve and saw x = +-sqrt(43) so I said that the line y=1 can’t be tangent to the curve if it intersects it at more than one point. Definition of a tangent line, yk. Do you think they give me full points for that?

[@turksvids]

Tangent lines can intersect curves more than once. Think of a cubic with a relative max and min, the tangents at the max and min will intersect the curve again.

[@lyonkang7402]

@@turksvids yeah that makes sense, but since the curve in the problem is an ellipse do you think i have an argument to stand on?

[@Floral_skies2727]

Okay, so b and c I did implicit differentiation I thinkk, might’ve gotten partial credit. Now for part d, I literally knew it was related rates and I did it but I simplified wrong. I wrote related rates as well to show them I knew what I was solving for. Will I at least get partial credit? Those were the only two parts I skipped on the whole non calc section, everything else was alright.

[@turksvids]

we'll see. could be eligible for set up points. if you found the correct derivative and just flubbed the subbing in/solving part, i think you'll get some points. don't forget that you can miss quite a few points and still earn a great score!

[@Retro3]

If I said No to B and C but my reasoning is wrong do I at least get some points?

[@nicolasgaguirre3411]

i sure hope so bro i’m in the same boat

[@AshvinJaishankar]

for part d, could you use the Chain Rule: (dy/dt) = (dy/dx)*(dx/dt) as an alternative approach?

[@turksvids]

yes, for sure! that's my "favorite way that i wish i would ever remember to use!" good catch!

[@davy1220]

I forgot the +- 🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🥵🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬🤬

[@Tharealwunkydunks1]

i'm cooked