[Math] The minimum and the maximum of $y=\sin^2x/(1+\cos^2x)$

Question

I was asked to find the minimum and maximum values ​​of the functions:

1. $y=\sin^2x/(1+\cos^2x)$;
2. $y=\sin^2x-\cos^4x$.

What I did so far:

1. $y' = 2\sin(2x)/(1+\cos^2x)^2$
   How do I check if they are suspicious extrema points? After this function is cyclical and therefore only section that is not $(-\infty,\infty)$ can there be a local minimum/maximum.

2. $y' = \sin(2x)+4\cos^3(x)\cdot\sin(x)$

Any suggestions?

Answer 1

Hint: $y=f(x)$ has maximum or minimum when $y'=0$.