Question

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

Answer 1

Hello,

Critical points of the function `k` are the numbers `t` which are solutions of `k'(t)=0`.

Here, `k(t) = (t^2+1)^{-1/2}`, therefore `k'(t) = -\frac{1}{2}(t^2+1)^{-3/2}\times (2t)`.

So, `k'(t) = 0 iff t=0`. The only critical point of `k` is `t=0`.