Answer to Question #108922 in Calculus for awesh

Question

Trace the curve y=(x^2-1)^1/3 and state all the properties you use to trace it

Answer 1

1.Even and continuous function

2.$y=0$ if $x=1,x=-1$

3.$y'=\frac{2x}{3}(x^2-1)^{-2/3},$ if $x=0$ then $y'=0$ hence $x=0$ is point of global minimum

$y(0)=-1$

4.$x=1,x=-1$ is stationar points, $y'(1),y'(-1)$ does not exist, hence $x=1,x=-1$

is points of inflection

5.If $x<-1,x>1 ,$ $y$ is concave downwards, $x>-1$ and $x<1$ , $y$ is concave upwards