Finding Extrema

If $x=3$  is a critical point of  $f\left(x\right),$ and  $f''\left(x\right)\ =\ e^{-x}\left(x^2-2x-4\right)$ then $x=3$   is a 

If   $x=0.5$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \cos^2x\cdot\ln x$  then  $x=0.5$  is a 

If   $x=e$  is a critical point of  $f\left(x\right)$  and  $f''\left(x\right)\ =\ \ln\left(x\right)-1$  then  $x=e$  is a 

 Which of the following is NOT a critical point of $f\left(x\right)\ =\ e^x\cdot x^2$ ?

Which of the following are NOT critical points of $f\left(x\right)\ =\ \ln\left(\cos\left(x\right)\right)$ ? 

Which of the following are NOT critical points of $f\left(x\right)\ =3^{4^x}$ ?

 How many critical points does the function $f\left(x\right)\ =\frac{\sin x}{x}$ have (on its entire domain)?

How many critical points does the function $f\left(x\right)\ =\ e^x\cdot x^3$  have? 

Where does the global maximum of $f\left(x\right)\ =\ e^{-x^2}$  occur on  $\left[-1,2\right]$ ? 

Where does the global minimum of  $f\left(x\right)\ =\ x^3-6x^2$  occur on the interval $\left[-2,6.5\right]$ ?