Find possible values of 'a' such that f(x) `=e^(2x) -2(a^(2) -21) e^(x)+ 8x+5` is monotonically increasing for `x in R.`

Explanation

`f(x) =e^(2x)-2(a^(2) -21) e^(x)+8x +5`
`f(x) =2e^(2x)- 2(a^(2) -21) e^(x) +8 ge 0 , AA c x in R`
`rArr " " e^(x) +(4)/(e^(x)) ge a^(2) -21`
`4 ge a^(2) -21 " "(":." e^(x) +(4)/(e^(x)) ge4)`
`rArr" " a in [-5,5]`