What are the critical values, if any, of  f(x)= sin^2x +cos^2x in [0,oo]?

Mar 16, 2016

I'd say that every number in $\left[0 , \infty\right)$ is a critical value.
$f \left(x\right) = {\sin}^{2} x + {\cos}^{2} x = 1$
So $f ' \left(x\right) = 0$
The critical values of $f$ are the numbers in the domain of $f$ at which the derivative either does not exist or the derivative is $0$. Since the derivative is $0$ for all numbers in the domain, I would say that every number in the domain is a critical value.