5.2 Relative Extrema & The 1st Derivative Test

5.2 Relative Extrema &

The 1st Derivative Test

Directions: Find the notes pictured to the right. Watch the video, take notes, and then try the practice problems.

Should you have Questions feel free to rejoin the Zoom session!

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Practice Problems

• Complete the two practice problems on this notes sheet!

• Enter your answers in to see how you did.

• Check you work.

• Come back to Zoom if you have any questions!

Multiple Select

Select ALL of the following that are crtical values in Example #1. 

• $x=0$

• $x=3$

• $x=9$

• $x=-3$

• $x=-9$

Fill in the Blank

State where the function in Example #1 is increasing.

**Type your answer with no spaces, use inf and -inf!**

Fill in the Blank

State where the function in Example #1 is decreasing.

**Type your answer with no spaces, use inf and -inf!**

Multiple Select

Select ALL of the following x-values where there is a relative maximum in Example #1.

• $x=0$

• $x=3$

• $x=9$

• $x=-3$

• $x=-9$

Multiple Select

Select ALL of the following x-values where there is a relative minimum in Example #1.

• $x=0$

• $x=3$

• $x=9$

• $x=-3$

• $x=-9$

Multiple Select

Select ALL of the following that are crtical values in Example #2. 

• $x=0$

•  $x=2$ 

•  $x=-2$ 

•  $x=4$ 

•  $x=-4$ 

Fill in the Blank

State where the function in Example #2 is increasing.

**Type your answer with no spaces, use inf and -inf!**

Fill in the Blank

State where the function in Example #2 is decreasing.

**Type your answer with no spaces, use inf and -inf!**

Multiple Select

Select ALL of the following x-values where there is a relative maximum in Example #2.

• $x=0$

•  $x=2$ 

•  $x=4$ 

•  $x=-4$ 

• There is no relative maximum.

Multiple Select

Select ALL of the following x-values where there is a relative minimum in Example #2.

• $x=0$

•  $x=2$ 

•  $x=4$ 

•  $x=-4$ 

• There is no relative minimum.

Open Ended

What is one question you still have about finding relative extrema for functions using the first derivative test?