Question

(18 pts) Find the absolute extreme values of f(x) = 2 cos x - sin 2x on [0, 21). (24 pts) If a ball is thrown vertically upward with a velocity of 160 feet per second, then its height after t seconds is h(t) = -16t2 + 160t. a. Find the average velocity of the ball during the first 5 seconds. b. Use the Mean Value Theorem to verify that at some time during the first 5 seconds the instantaneous velocity of the ball equals its average velocity. Find that time.

Answer 1

1 F1x) = 26857 - sin a3 on 10, pā) differenciate with respect "X" F'LZ): -sinn - (05pali? - your conti col point Flx) =0 ta sinut 2005 272) = 0 sina = -losaa Sinn =- [1-asina] sinn - 2 sin²x = -1 Sin naa sinzat zo 2 sinta - Sinal=0 suot is = 1 t 3 २५२ dina : 1tr78 282

sinn - 4 na sint (-a) ma Hill and sinnal na Æ , 312 Critical value aure F(P) = 2605) - sin o F(75) = 2005 (-sin ARX EA) F(7) = -2.598 (minimum) F1 115) = Rros photos - Sin(014) a 2.598 absolute Maximum on (0, 27)

TT/6 (111/6, 2.598) (0,2) (1.571.0) (77/6, -2.598)