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

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Answer 1 · 2015-02-19T17:21:19

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 $t=0$ .

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