Question

[12] The position function of a fly is given by F(t)=(+2,75,2 – 16t). When is the speed of the fly at a minimum? Round to the nearest whole number. The speed is at a minimum at time, t =

Answer 1

6) Given! < +² 7 t. &2-163 To find belocity differentiate above function V = d (8 (t)) <th It, t² 4627 elt ot < df2 dt 7 dt चना (+² -164) (senya hah) < 27,7 act2 – 16 ct - 16 dt et < 27,7 get a 16.3 Sheed: 1 VC4) (2+2 of (78+ (2t - 16) 2 4t² & 49 of 4t2 64t of 256 |wa| 8 t2 64t of 305. 842.64 44305 To minimize the the speed, minimize for 40 f(t) = 842-64 + + 305. Let

Differentiate above function. f'(4)=(8+2-64 + + 305) 8d2 - 64 dt d (305) at dt dt 8.gta 64 Equate f'(t)=0 167 - 64 ta 4. Sign analysis of f'ct) ove of ve decreasing increasing & -4. min, Art & = 4, get minimum value of of Ct). it gives also minimum value of the speed | VCH) 842-644 4305 To get minimum speed put t = 4 1 (4) 8 (4)? - 64(4) 4 305 128 - 25 6 of 305. 174 Hence At & = 4 & = 4 get minimum speed and it is equal to viac f = 4 AND