I have a function f : $[-1,1]\rightarrow R$. If I know that f is monotonic increasing in [-1,0] and in [0,1] then is monotonic increasing in all [-1,1]?
I know that this isn't true for the function when is injective ( for example $f(x)=x^2$ ) i.e if f is injective in [-1,0] and in [0,1] then can not be injective in all [-1,1]