Absolute and Local/Relative Extrema

Select all that are true:

• There is a local max at $x=-3$

  
  

• The graph has an absolute minimum

• The graph has two relative extrema

•  $f'\left(-2\right)=0$ 

• The graph shows a differentiable function.

Identify the local minimum of the graph:

• none

• $y=0$

• $-\infty$

• $x=2$

Select all that are true:

•  there is an absolute maximum at $x=1$ 

•  there is a relative maximum at $x=1$ 
  

•  there is an absolute maximum of $y=0$ 
  

• there is no local or absolute minimum

What are the local minimums of the graph? Just enter numbers, separated by a comma:

(a)  

If $\left(a,\ b\right)$  is a local extrema, then what will be true about  $f'\left(a\right)$ ?

•  $f'\left(a\right)$  is positive
  

•  $f'\left(a\right)$ is negative

•  $f'\left(a\right)=0$  

• Cannot be determined

Suppose we restrict the domain of the graphed function to  $-5\le x\le0$ . Where does the absolute minimum occur?

•  $-4$  
  

•  $-2$  
  

•  $0$  
  

•  $-3$  
  

• Does Not Exist

Suppose we restrict the domain of the graphed function to  $-5\le x\le0$ . What is the absolute minimum?

•  $-4$  
  

•  $-2$  
  

•  $0$  
  

•  $-3$  
  

• Does Not Exist

The function above is defined on $-\frac{\pi}{4}<x<\frac{π}{2}$ . Select all that are true: 

• The function has an absolute minimum.

• The function has an absolute maximum.

• The function has a local minimum.

• The function has a local maximum.

The function above is defined on $-\frac{\pi}{4}\le x\le\frac{π}{2}$ . Select all that are true: 

• The function has an absolute minimum.

• The function has an absolute maximum.

• The function has a local minimum.

• The function has a local maximum.