Extrema and Function Analysis (3.2 CA)

Extrema and Function Analysis

3.2 Corrective Assignment Examples

Multiple Choice

What is an Absolute Maximum / Minimum

• The highest/lowest point for the entire function/graph.

• Any peak in the function

• The part that tends to infinity or negative infinity of the graph

Multiple Choice

What is a local max/min?

• A point higher/lower than its surrounding values. (a peak)

• The second highest/lowest point in the graph

Multiple Choice

Find the domain for the graphed function

• $\left[\infty,-1\right]\cup\left(2,\infty\right)$

• $\left(-\infty,\infty\right)$

• $\left(-4,-1\right]\cup\left(2,\infty\right)$

 $\left(-\infty,-1\right]\cup\left(2,\infty\right)$  

Multiple Choice

What is the Absolute Max/Min of the graphed function?

• N/A

• (2, -4) is an Absolute Min

• (-1,1) is an Absolute Max

• $\infty$

Multiple Select

What is the Local Max/Min of the graphed function? (select all that apply)

• N/A

• (2, -4) is a Local Min

• (-1,1) is an Local Max

• (-2,-1) is a Local Min

Multiple Select

On what intervals is the Function Increasing and Decreasing? (select all that apply)

• Increasing:  $\left(-2,\ 1\right)\cup\left(2,\ \infty\right)$  

• Decreasing:  $\left(-\infty,\ -2\right)$  

• It's a constant function

• Increasing:  $\left(-2,\ \infty\right)$  

• Decreasing:  $\left(-\infty,\ 2\right)$  

As x goes to negative and positive infinity, how does the graph behave?

Open Ended

What anime (or film) do you recommend to watch?

Is there any part of the function that will affect its domain?

Multiple Choice

What inequality can we build to find the domain of the function?

• $x+5\ge0$

• $x+5>0$

• $x^2+2\le0$

• All real numbers

Multiple Select

Identify the Absolute Max/Min of the function.

• Absolute Min at

  (0.098, -2.247)

• N/A

• Absolute Max at

  (-4.098, 7.025)

• Absolute Min at

  (-5,0)

Multiple Select

Identify the Local Max/Min of the function that are not absolutes.

• Local Min at

  (0.098, -2.247)

• N/A

• Local Max at

  (-4.098, 7.025)

• Local Min at

  (-5,0)

Multiple Select

When is the graph increasing and decreasing?

• Increasing:
  $\left(-5,\ -4.098\right)\cup\left(0.098,\ \infty\right)$

• Decreasing:
  $\left(-4.098,\ 0.098\right)$
  

• Increasing: $\left(-5,\ \infty\right)$

• the function is constant

Poll

Is there a skill you practice on your own? Something you see yourself doing 20+ years from now.

• Study a subject or trade

• Learn a musical instrument

• Practice a sport

• Visual Arts

• Other