Derivative tests question Show that $k(x) = \sin^{-1}(x)$ has $0$ inflections $2$ critical points $0$ max/min
I find that the first derivative is $$\frac{1}{\sqrt{1-x^2}}$$
Second derivative is $$\frac{x}{(1-x^2)\sqrt{1-x^2}}$$
I don't know why it has $2$ critical points, I can find only one at second derivative which $x = 0$. I don't know the other one.
There is no min/man because I can't find $x$ values in first derivative.


In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0 or undefined

As you can easily see, $f'(x)$ is undefined on $x=1$ and $x=-1$.
I think you might have misunderstood the concept of a critical point for that of an inflection point.
