Find the maximum and the minimum values of `f(x)=3x^2+6x+8,\ \ x in R` , if any.

Explanation

Given, `f(x)=3x^2+6x+8,\ \ x in R`


`f(x)=3(x^2+2x+1)+5`


`f(x)=3(x+1)^2+5`


`3(x+1)^2 ge 0` for all `x in R`


`3(x+1)^2+5 ge 5` for all `x in R`


`f(x) ge f(-1)` for `x in R`


Minimum value of function is `5` which at `x=-1`


There is no such maximum value as we put any value of `R`, maximum value does not exist