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if f(x) =2e^(x) -ae^(-x) +(2a +1) x-3 mo...

if f(x) `=2e^(x) -ae^(-x) +(2a +1) x-3` monotonically increases for `AA x in R` then the minimum value of 'a' is

A

2

B

1

C

0

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
`f'(x)=2e^(x)+ke^(-x)(2k+1)`
`=2e^(x)+(k)/(e^(x))+(2k+1)`
`=(2(e^(x))^(2)+k(2k+1)e^(x))/(e^(x))`
Now f(x) is monotonically increasing.
`rArr" "f'(x)le0" i.e., "2y^(2)+(2k+1)y+kle0`
where `y=e^(x)`
`therefore" "2y^(2)(2k+1)y+k le 0` for all positive value of y.
For the `k le0`.
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