2023 AP Calculus AB FRQ #4

The function f is defined on the closed interval [−2, 8] and satisfies f(2) = 1. The graph of f’, the derivative of f, consists of two line segments and a semicircle, as shown in the figure.
(a) Does f have a relative minimum, a relative maximum, or neither at x = 6 ? Give a reason for your answer.
(b) On what open intervals, if any, is the graph of f concave down? Give a reason for your answer.
(c) Find the value of lim x→2 (6 * f(x) − 3x) / (x^2 − 5x + 6), or show that it does not exist. Justify your answer.
(d) Find the absolute minimum value of f on the closed interval [−2, 8]. Justify your answer.
Intro: 00:00
Problem a: 00:19
Problem b: 02:23
Problem c: 04:37
Problem d: 08:07

[@NickiNicker]

omg thank you so much olga I'm your second biggest fan!!!

[@OlgaAndreevaVideos]

🫶

[@fatherofall7036]

I'm your biggest fan

[@OlgaAndreevaVideos]

🫶

[@rabbit-istudios5444]

Dude for the last question looking at the graph you can see that x = 2 is the only x coordinate where it is a candidate for a absolute minimum value. Thus it will be the only absolute minimum value in the graph. Therefore the absolute minimum value is f(2) = 1. (f(2) = 1 is given in the question itself).

[@user-bm7ds4mi7k]

problem d is wrong LOL

[@fatherofall7036]

Wrong.

[@NickiNicker]

wrong. denied.