AP Calculus AB: Exam Prep Graph Analysis FRQs

[@iMareisha]

Please do more AP Calc AB review! They are really helpful!

[@kakequinn]

Extremely helpful. A handful of your AP calculus ab material was on the exam this year! And doing these are a real confidence booster when your able to work them on your own and get them correct.

[@joaquino5438]

for letter d, wouldn't your P.O.I be x=-2 instead of x=-1? since it changes concvity at x=-2 please correct me if I'm wrong

[@nickkerr191]

you're correct

[@kingkunta9412]

I thought points of inflection was when the concavity changes so why did you check where there is a horizontal tangent?

[@parkerm24]

at 8:20 for number 4 2011, why don't you also check if the endpoints are maximums because doesn't it say absolute?

[@jsandov6]

Parker, remember that it’s asking specifically for the point of inflection and we got that from taking the derivative and setting it equal to zero. But you are also right, it doesn’t ask for the absolute max or min. Good job! Hope it helps.

[@alexgeorge1090]

When you are doing letter c around 13:00, How would POI at x=0 work. Doesn't it classify as a CUSP meaning we can't use it? I understand that it does match the f''(x)=0 requirement though.

[@jsandov6]

That's a great question Alex. The key lies in the question. Is there a point of inflection at x = 0? Yes, because the graph changes from increasing (positive slope) to decreasing (negative slope) but can we find the value of that point of inflection? No, because it's a cusp. Think of the graph y = x^1/3, similar thing, there's a change in concavity at x=0 but at x=0 its value is undefined. Hope this helps!

[@ColtraneTurnaroundBlues]

For b in the first frq, it seems like you dont have to check the endpoints such as -4 and 3, does that mean you only check the endpoints for maxiumum if it is asking for the value? For c in the first frq, can you also get the point by saying g'(x) goes from increasing to decreasing?

[@StephanieO-k7h]

I think that the justification using end points is necessary (according to the scoring guidelines in similar problems) to earn the point as abs max/min also needs to consider end points. As for c, since g``(x) is the point of inflection for function g, g``(x)=f`(x)=0 at x=0 AND f`(x) changes signs (from increasing to decreasing) is also acceptable for the justification.

[@jsandov6]

EW, that’s correct, you check the endpoints when it’s asking for the value. Also, you can say g’(x) goes from increasing to decreasing. Great job!!

[@adi_yerabati]

Points of inflection at 28:24 is x = -2, x= 0 and x = 1. You wrote x = -1 rather than x = -2.

[@jsandov6]

Awww man!, you're right, should be x = -2 not x = -1. Good looking out. Thank you!