Given the properties of the first and second order derivatives of functions, and proving the relevant inequalities.

Question

Known $ \ 0<a<b,f(a)=0, and $ $\ f^{'}(x)>0,f^{''}(x)<0$ are true when $x\in (a,b)$. Please prove:$$f^{'}(x)+2xf^{''}(x)\le0,x \in (a,b)$$ We find $f(x)=x^{1/2}-1,x\in (1,2)$ meet conditions and conclusions. However, we do not prove the conclusion.