IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

Sushmi

The intervals of decrease and increase of the function f(x) = e^x / x are respectively

( -

, 0 )

( 0 , 1 ) and ( 1 ,

)

Then which one is correct ,

a.) p.e^q < q.e^p if 0 < p < q b.) p.e^q > q.e^p if 1 < p < q

c.) q.e^p < p.e^q if o < p < q < 1 d.) q.e^p>p.e^q if 0< q < p < 1

Werewolf

B

since the function is increasing in (1,

) so

if 1 < p < q then e^q/q> e^p/p => e^qp> e^pq

raulrag009

ans is (B) and (D)

Werewolf

How can there be two answers , she asked "which ONE is correct"

computer001

jus diff n chk the intervals where inc n dec
i dont think its ne pt solvin 4 the soln..

Sushmi

Sorry for the late reply, there was a power cut here

answer given is C

uday_zingtudor

hey

how wud the answer be C when both the options C and D imply the same????

For ur kind information!!!

U can't have a right answer with those options.

Thank u

edit: sorry!! dint check the B option properly 'twas also right

joyfrancis

For decreasing function if a<b ..f(a)>f(b) and for increasing funtions... f(a)<f(b)...

option A :

Range of p and q : (-inf,0)...:decreasing function...so if p<q then f(p)>f(q)... $\frac{e^p}{p} > \frac{e^q}{q}$ ...which is the opposite of the given option....hence A is false...

option B :

Range : (1,inf).....:increasin'....so if p<q ,...f(p)<f(q)... $\frac{e^p}{p} < \frac{e^q}{q}$ ...so B is right

option C :

Range : (0,1)...decreasin'...so if p<q ....f(p)>f(q).... $\frac{e^p}{p} > \frac{e^q}{q}$ ....so C is incorrect

option D:

Range ; (0,1)....decreasing'...if p>q...f(p)<f(q)... $\frac{e^p}{p} < \frac{e^q}{q}$ ..so D is also incorrect.

So the only correct option is B

eistien

hey B is only right Francis is rite!!! i too get the same answer!!!!

C and D are obiously false!!!!

check your signs maybe some typing mistake might have been made!!!

eistien

dupilcate

eistien

duplicate

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