# How do you find all critical points (if any) if k(t)=1/sqrt(t^2 +1)?

Critical points of the function $k$ are the numbers $t$ which are solutions of $k ' \left(t\right) = 0$.
Here, $k \left(t\right) = {\left({t}^{2} + 1\right)}^{- \frac{1}{2}}$, therefore $k ' \left(t\right) = - \setminus \frac{1}{2} {\left({t}^{2} + 1\right)}^{- \frac{3}{2}} \setminus \times \left(2 t\right)$.
So, $k ' \left(t\right) = 0 \iff t = 0$. The only critical point of $k$ is $t = 0$.