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Differential Calculus

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1 Apr 2009 16:30:43 IST

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300

good ques... rates assured.......

None

Let f and g be non increasing and non decreasing functions respectively from [0, infinity) to [0, infinity)

and h(x)=f(g(x)) ,h(0)=0 then in [0 , infinity), h(x)-h(1) is...........

a) <0

b)>0

c)=0

d)increasing

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Comments (6)

ar rehman

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Joined: 24 Feb 2009

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1 Apr 2009 16:34:24 IST

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try yaar!

atlest give some hint......

saharsha kumar keshkar

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1 Apr 2009 16:40:51 IST

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wats the answer is it 0. i.e option (c)...

if not then wats the answer...

ar rehman

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1 Apr 2009 16:42:09 IST

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ya! it is (c)

solution please......

saharsha kumar keshkar

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1 Apr 2009 16:56:09 IST

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solution:

f:[0, ) [0,) , g[0,)[0,)

and h(x)= f(g(x))

therefore,

h: [0,)[0,)

therfore,

h'(x)=f'(g(x))*g'(x) <=0 ........(since f'(x)<=0 and g'(x)>= 0)

h(x) os monotonically decreasing function..

x>=0 .. h(x)<=h(0)

h(x)<=0 in [0,)............becoz given that h(0)=0........(1)

also...h:[0,)[0,)

therfore h(x)>= 0 in [0,)..........(2)

from (1) and (2)....h(x)=0 in [0,)

hence....h(x)-h(1)=0-0=0.

hence answer is (c).

nudge if any doubt..

bladeX -rise of a new sun

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1 Apr 2009 17:02:08 IST

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THE QS. IS VERY GOOD.NOW F IS NON INCREASING AND G IS NON DECREASING .F' <=0 AND G' >=0F(G(X)) IS ALWAYS BETWEEN O AND INFINITY (COMMON SENSE YOU CAN CHECK IT )H(X) = F(G(X))COMPOSITION OF A NON DECR AND NON INC FUNCTION IS NON DECREASINGSO H(X)' <=0 ...........1NOW H(0) = 0 ...........2 HENCE FOR ALL POSITIVE VALUE OF X H(X) <=0conclusion of 1 and 2 but H(x) >=0so only way is that H(x) = 0so H(x) - H(1) = 0

ar rehman

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1 Apr 2009 17:43:14 IST

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THANX GUY's!

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