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Find the range of values of a if f(x)=2e...

Find the range of values of `a` if `f(x)=2e^x-a e^(-x)+(2a+1)x-3` is monotonically increasing for all values of `xdot`

Text Solution

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f(x) =`2e^(+)+ae^(-x)+ae^(-x)+2a+1`
`=e^(-x)(2e^(2x))+(2a+1)e^(x)+a)`
`=e^(-x)(e^(x)+a)(2e^(e^(x))+1)`
For f(x) to be increasing f(x) to the increasing `f(x)ge 0 forall` x in R
`rarr e^(x)+age0forall` x in R
`rarr age-e^(x)forall` x in R
`rarr age0`
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