Question

(2) Consider the two functions, a(t) and (t), plotted below. pact) Abct) Determine the maximum value of a(t) .b(t). (20 points)

Answer 1

nat) Host d t 1. let ya= a(6) & 6E) = f(r) art-1)dt. b♡ af?) dľ IT -2 - a (t-1) (t-2 (ty 6(%) = 1 1 2 (3-7),o=18 lo, else for tal i alt-7) nl 1058 D > 1 H

g (t)=0 no overlap 1 YE)=0 for tal ist2 a (t-1) b@) Ha est ź(3-4) 4-2 (t-1) it. o ? 96) = S(+) (3-1)dt it-1 0-6(1-=(1-1) = +36-3 - + Y(t) = -th +46-7/22 , Istra for a st<4

alt-") 6-10 3 1 of 3 tl Helt 546)(1-3)dy t-2 - Yound to fr-ca - 34-1)= }&•v*)-[34-246-38] + [3t3 ***]<foto (4-4-2) - (55--8] = -6 + 4.5 y El= 4,5-t for ast<4

675h &>75h sizlt pe- 1 2 - 10th 32+ 35- - [B-76 + 1] - 9th = [42+z-ž-9-14]-sh [cept - (2-08 ]-[6-6] - 2P (4-6) (7) * 5 =15 + telp & LE (2-7BV G>757

t75 palt-?) EL + 3 62 (21) t (no overlap). 96)=0 Y(t)= | 4t-tho - 7 / Istaa 405-t 2st24 t²_56+12.5, 4 st 5 o relse 90)-0, 7(2) = 215, 9(3)= 15 y (4)=0.9, y (5)=0 . : Maximum value § 2.5 max (act) *b (t)) = 2015 427=25