Find the maximum and minimum values of `f(x)=|sin4x+3|` on `R` , if any, without using derivatives.

Explanation

`f(x)=|sin4+3|`

we know ,
`
-1 le sin4x le 1`
`
therefore 2 le sin4x +3 le 4`

`
therefore 2 le |sin4x +3| le 4`

Hence, the maximum and minimum values of f are 4 and 2 respectively