Saddle point / Local Maxima

Question

What I understand from the question is they're asking us what is $x = 3$ called, to which I'm answering a saddle point / critical point / stationary point. But $x=3$ is also a local minimum for the function when we double differentiate and put the value.

What would be the appropriate answer to this question? Where am I going wrong with the understanding? Please help

Question

Definition

Answer 1

Basically you are on correct track. It is a critical point associated with a minimum at $X=3$, but not an inflexion or saddle point, as can be checked employing its second derivative.

Answer 2

There's no typo, it states that the value of the slope has value $0$ at $x=3$, i.e., $f'(3)=0$ which is true

$f'(x)=8x-24$

$f''(x)=8>0$ $\forall$ $x$

The second derivative is concave up at $x=3$, so it is a minimum