HW$-4-3$: Problem $10$

$(9$ points$)$

Answer the following questions for the function

$f(x)=x\sqrt[\phantom{2}]{x^{2}1}$

defined on the interval $-5,5.$

a$.)f(x)$ is concave down on the open interval $$

b$.)f(x)$ is concave up on the open interval

c$.)$ The minimum for this function occurs at

d$.)$ The maximum for this function occurs at