Proof

IIT JEE 2015 Guidance › Calculus questions › Proof

Let g'(x)>0 and f'(x)<0 for all x Îµ R
then prove that g(f(x+1))<g(f(x-1))

#Mathematics #Calculus

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7 Answers

62

Lokesh Verma ·2009-08-28 10:11:16

Is this the hint or the solution ;)

f(x+1)< f(x-1)

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66

kaymant ·2009-08-28 10:12:26

g'(x)>0 => g(x) is strictly increasing
f'(x)<0 => f(x) is strictly decreasing
Also for all real x,
x+1 > x-1

so how do f(x+1) and f(x-1) compare?

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62

Lokesh Verma ·2009-08-28 10:13:15

oh Kaymant sir, you have already posted a reply :)

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66

kaymant ·2009-08-28 10:15:05

interesting timing... generally I don't find you at this time.. :)

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champ ·2009-08-28 10:15:41

Thank you :-)

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62

Lokesh Verma ·2009-08-28 10:17:23

yup i come online in the day time...

btw i will try to give you a call and visit you tomorrow... (Hopefully finally :)

Unfortunately the classes continute till late and having worked for 16 odd hours (with the travel) we feel very tired :)

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kaymant ·2009-08-28 10:25:45

Hmm...That's really hard work... :)
.. and yes.. hopefully.:)

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Your Answer

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