If f(x) = 1 + 2xif 0?x?1 , f(x) = 8 - 5x , 1< x 2, f(x) = 3x - 8 if 2< x less or equal to 3 & g(x) = [0][x] f(t) dt x belongs to [0,3] theng(x) increasing and decreasing in?
Ans: increasing in (0,8/5) & (8/3) and decreasing in (8/5,8/3)
g'(x) = f(x) It is positive from 0 to 1 so g(x) is increasing In 1 to 2 f(x) is positive from 1 to 8/t So it si increasing from 1 to 8/5 and decreasing from 8/5 to 2 In 2 to 3 f(x) is negative from 2 to 8/3 So here g(x) is decreasing and from 8/3 to 3 f(x) is positive so here g(x) is increasing
Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi
Moderation Team
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2, f(x) = 3x - 8 if 2< x less or equal to 3 & g(x) = [0]
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