2024 Calc AB & Calc BC FRQ #1

Free Response Question #1 from the 2024 AP Calculus AB and AP Calculus BC exam.

Table problem. Calculator active.
Average rate of change; units of derivative; average value; Left Riemann sum; fundamental theorem of calculus (FTC); increasing or decreasing rate using second derivative

[turksvids]

Scoring guidelines are out! Part d is right.

[basketballpro]

For part d, the temperature should be changing at a decreasing rate because c’ and c” are in opposite directions I would think just like speed decreases when velocity and acceleration are in different directions.

[luccohen]

For part D., would the rate not be decreasing, considering the fact that C'(t) is negative for this interval? Thus, the rate of change in temperature would be approaching 0, rather than speeding up.

[Vrexell]

Ive found multiple other teachers solving this problem (1d) on social media and they say decreasing because you interpret the rates as an absolute value

[pablonerudaishidingincuba]

For 1d, I said the rate was decreasing, I might have misinterpreted the problem. In the question, the rate of change would be the absolute value of the derivative (since it is not making a distinction between increasing/decreasing temperature, only increasing/decreasing rate). If the absolute value of the derivative was decreasing, then the rate of change would be decreasing. If C’(t) is negative while C”(t) is positive, then |C’(t)| would be decreasing.

[cheaponation]

Turk my goat

having the same answer for d fills me with confidence.

[icii]

for question 1 wouldn’t it have to be at a decreasing rate because c’(t) is always negative so it’s absolute value is decreasing over the interval because c’’(t) is positive?

[imnobody]

I feel like the first half of this year's FRQs were super similar to last year's FRQs which makes me feel good bc I spent most of my time studying the 2023 FRQs

[shotsquad]

I feel like your explanation would only apply if the first derivative was also positive. Then the rate at which it is changing would be an increasing rate.

[goat]

bro you were such a help in my studying i wish i had found your channel earlier in the class thank you for the great resources 🔥🔥

[fergi]

Since C'(t) is negative and C''(t) is positive, isn't the temperature changing at a decreasing rate for part (d)?

[speedster]

For part d, since the first derivative is negative and second derivative is positive, doesn't that mean the temp is going down at a decreasing rate?

[Dollaboi]

Second derivative being positive means first derivative is increasing

[stephen]

I disagree with your 1d.) the problem is asking about the temperature of the coffee and the rate of the coffee. For 12<t<20, C' < 0 and C''(t) > 0. Therefore, the rate of change of the coffee is getting slower and decreasing, therefore the TEMPERATURE of the coffee is changing at a decreasing rate (aka the coffee's temperature is getting colder slowly)

[Dollaboi]

For 1b. If I had 985 written and the work for the Reimen sum but ended up dividing by 12 at the end to use in the interpretation would I still get the point for the approximation and the Reimen sum

[mogus]

These FRQs are different to the ones I got? Are there different sets?

[glacius]

I got changing at a decreasing rate because the 2nd derivative is positive but the 1st derivative is negative

[moomoo-jtyq]

For part d, wouldn’t the temperature of the coffee be changing at a decreasing rate because C’(t) is less than 0 and C’’(t) is greater than 0?

[shotsquad]

I’m so lost why d on BC isn’t decreasing. It’s asking about the rate at which the coffee is changing. So If the first derivative is negative from 12 to 20 that means that the coffee temp is decreasing but if the 2nd derivative is positive then that means that the first derivative is has a positive slope and bc it’s negative that means it’s getting less negative from 12 to 20. If the first derivative gets less negative doesn’t that mean the temp of the coffee is changing at a slower rate now? The 1st derivative at t=12 is about -2.3 and at t=20 it’s about -1.5. That means it’s now cooling slower than it was prevously so the rate at which is it changing is decreasing

[potatotree]

was literally cooked, so depressed now omg 😭