2021 AP Calculus AB FRQ #5

Consider the function y = f(x) whose curve is given by the equation 2y^2 − 6 = y * sin(x) for y is greater than 0. (a) Show that dy/dx = y * cos x / 4y − sin(x)
(b) Write an equation for the line tangent to the curve at the point (0, sqrt(3)).
(c) For 0 to pi and y is greater than 0, find the coordinates of the point where the line tangent to the curve is horizontal.
(d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer.
Timestamps
Intro: 00:00
Part a: 00:14
Part b: 02:03
Part c: 04:44
Part d: 08:20

[@gtc4189]

For part c you use the quadratic formula instead of factoring it into (2y+3)(y-2). It saves time (to factor) in this scenario but do you think that for the exam it would be worth it to attempt to factor quadratic equations or just go straight to the quadratic equation?

[@OlgaAndreevaVideos]

I am relatively bad at factoring equations, so I opt for the quadratic equation in situations like this haha, so I would say it depends on your level of comfort with factoring.
When I took the test (way back in the day) I didn't feel too much time pressure, but if you're timing yourself taking practice exams and finding that you need all the time you can get, attempting to factor might be worthwhile!