2023 AP Calculus AB and BC Free Response #4

Walkthrough of the 2023 AP Calculus AB and BC FRQ #4

[AllenTsaoSTEMCoach]

Corrections:

Part c) I did an arithmetic mistake. The limit should be 3.

Part d) f(8) should equal 11-2pi.

[michaelandino]

there’s a mistake with part d) the area from 4 to 8 is 8-2pi but you forgot to include (even though you did the calculation) the area from 2 to 4 which is 2, so the area from 2 to 8 is 10-2pi, and if you add f(2) which is 1 that gives you that f(8) = 11-2pi

[tylercollins]

The limit for 4c should be equal to 3!

[Spoopyyy]

This problem was a nice break from the rest kinda relaxing ngl 😅

[moniso]

I said -3 as well for the limit (sign mistake, did arithmetic up until that + l'hopital correctly). Will I still get every point just minus the one for answer?

[vanessadeborah]

Messed up d 😭😭but everything else good

[razfn]

The denominator for frq #4 is 2(2)-5 correct? wouldnt the limit using lhopitsl be 3 using this computation?

[satvikpatel]

I believe C should be positive 3 denominators of limit is 2x-5 ->2(2)-5=-1

[andythepianoman]

Hey, Mr. Tsao. Just wanted to make you aware of the proper notation for full credit on part c:
lim (x->2) of 6f(x)-3x=0
lim(x->2) of x^2-5x+6=0
lim(x->2) of (6f(x)-3x)/(x^2-5x+6)-> 0/0, which is an indeterminate form. Therefore, L’Hospital’s rule can be applied. Great video though!

[vivianm]

is it okay if you didnt justify with a sign test for part a? like i just said it was neither bc the derivative doesnt switch signs

[jakeroly]

For part a, what if i wrote that it's because f'(x) did not change sign at x = 6

[chibuikemchinweze]

for part D would they take off a lot of points if I put the x value and not the y value

[TANMAN]

Part D took me forever and I didn't even get it correct. I was running out of room

[nightfall]

I think you messed up the limit on part D, you changed the -5 in the denominator to -3.

[abramtadros]

For part d, isn’t 8 a local max not local minimum ?

[spicyoreos]

For the minimum I put (2, 3) because I thought the answer for C was the y value at 2 😭

[nathanmckay]

FYI, you should be using the new way L'Hop needs to be written out as of 2022. Must show lim of numerator = 0 separate from lim of den = 0 before proceeding to lim of the derivatives.

[advaithvijayakumar]

For (d), instead of using the candidate test for absolute extrema, would it be acceptable to state the area under the f' curve is the least at x=2 and that f(2) = 1?

[stephanie-zqsz]

How many points do you think d would be worth?