Question

help me, pleaseee..
For any real number b, let f(b) denote the minimum of the function
| sin x + 2/(3 + sin x) + b |
find the minimum of f(b), for x and b real...

Answer 1

| sin x + 2/(3 + sin x) + b | = absolut of sin x + 2/(3 + sin x) + b

Answer 2

i think minimum value occurs when
b : -ve
sin x : +1

Answer 3

we can setup b as,
b = - [sinx + 2/(3+sinx) ]

then the minimum value is 0 !!