Find the maximum and the minimum values, if any, of the following functions `f(x)=sin3x+4,x in (-pi/2,pi/2)`

Explanation

Given functions
`f(x)=sin3x+4,x in (-pi/2,pi/2)`
we know `-1lesin3xle1`
`=>-1+4lesin3x+4le1+4`
`=>3lef(x)le5`
so, maximum`=5`
`sin3x+4=5`
`=>sin3x=1`
`=>3x=pi/2`
`=>x=pi/6`
minimum`=3`
`sin3x+4=3`
`=>sin3x=-1`
`=>3x=-pi/2`
`=>x=-pi/6`