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a)
N'(t) = 0
N' (t) = -10 t/ 4 + 20 = 0
-10t/4 = -20
t = 20 : 10/4 = 8
b)
-5/4 t² + 20t + 100 = 0
-5t² + 80t + 400 = 0
t² - 16 t -80 = 0
(t - 20)(t + 4) = 0
t = 20
c) n(t)= 1/2 (100) = 50
-5/4 t² +20t + 100 = 50
-5/4 t^2 + 20t + 50 = 0
5t^2 - 80t - 200 =0
t^2 - 16 t - 40 =0
(t-8)^2 = 40+64 = 104
t = 8 + √104= 8 + 2√26