Question

What is the maximum value of `(3-cosx)/(1+cosx)` for `0< x < (2pi)`?

Answer 1

`x_{max}=+infty`
`x_{min}=0`

Explanation:

The function has a vertical asymptote in `x=pi` and its maximum is when the denominator has the lowest value just for `x=+pi`, instead is minimum when the denominator is the biggest i.e. for `x=0` and `x=2pi`

The same conclusion could have been deduced by deriving the function and studying the sign of the first derivative!