Suppose $f"$ is continuous on $(-,).$

$($a$)$ If $f^{\text{'}}(-3)=0$ and $f^{\text{'}}(-3)=-5,$ what can you say about $f?$

At $x=-3,f$ has a local maximum.

At $x=-3,f$ has a local minimum.

At $x=-3,t$ has nether a maximum nor a minimum.

More information is needed to determine if $f$ has a maximum or minimum at $x=-3.$

$($b$)$ If $f(-1)=0$ and $f^{\text{'}}(-1)=0,$ what can you say about $f?$

At $x=-1,f$ has a local maximum.

At $x=-1,$ f has a local minimum.

At $x=-1,f$ has neither a maximum nor a minimum.

More information is needed to determine if $f$ has a maximum or minimum at $x=-1.$