Assume $\backslash ($ f $\backslash )$ is continuous for all real numbers, and the graph given below is of $\backslash ($ y$=$f$^\{\backslash$prime$\}($x$)\backslash ).$

$($a$)$ List the $\backslash ($ x $\backslash )-$values at which the graph of $\backslash ($ f $\backslash )$ has horizontal tangent lines if they exist. Note: The above graph is the derivative of $\backslash ($ f $\backslash )$ and you can check the "student hint" for more information about terminology.

$($Give your answer in the form of a comma$-$separated list. Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

$($b$)$ List the $\backslash ($ x $\backslash )-$values at which cusps occur if they exist. Note: The above graph is the derivative of $\backslash ($ f $\backslash )$ and you can check the "student hint" for more information about terminology.

$($Give your answer in the form of a comma$-$separated list. Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

$\backslash [$

x$=$

$\backslash ]$

$($c$)$ List the $\backslash ($ x $\backslash )-$values at which corners occur if they exist. Note: The above graph is the derivative of $\backslash ($ f $\backslash )$ and you can check the "student hint" for more information about terminology.

$($Give your answer in the form of a comma$-$separated list. Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

$\backslash [$

x$=1$

$\backslash ]$