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Let f(x)=e^((P+1)x)-e^(x) for real numbe...

Let `f(x)=e^((P+1)x)-e^(x)` for real number `Pgt0,` then
Let `g(t)=int_(t)^(t+1)f(x)e^(t-x)dx.` The value of `t=t_(P),` for which g(t) is minimum, is

A

`-log_(e).((e^(P-1)))/(P)`

B

`-(1)/(P)log_(e)((e^(P-1))/(P))`

C

`-(1)/(P)log_(e).(((P+1)(e^(P-1)))/(P))`

D

`-log_(e)((P+1)(e^(P)-1))`

Text Solution

Verified by Experts

The correct Answer is:
C
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