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The First and Second Derivative TestsPowerPoint Presentation

The First and Second Derivative Tests

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### The First and Second Derivative Tests

Today you will connect concavity with the sign of the second derivative.

Silent Board Game

Do NOT Talk!!!!

Each of you will label a characteristic on the sketch I am about to draw, one at a time, without talking. It is your job to label the curve as completely as possible. You may use descriptive words, symbolic notation, etc. Each person may only add ONE label to the curve.

Walk-A-Wave Challenge

- Can you walk a perfect sine wave?
- How can you “walk” so that that you get a nice curvy wave with points of inflection?
- How do you “walk” the concavity of the sine wave?
- When are you walking the fastest?
- When do you slow down?

How does the increasing or decreasing nature of a curve relate to the first derivative? The second derivative?

How does the concavity of the curve relate to the second derivative? The first derivative?

f. Does the direction you walk affect the concavity of the curve?

First & Second Derivative Tests relate to the first derivative? The second derivative?

- Apply your theories from the last problem to find where is increasing and decreasing. Where is it concave up? Concave down?

Points of Inflection relate to the first derivative? The second derivative?

A point of inflection is a point where concavity changes. Since the point of inflection deals with concavity, it must be related to the second derivative.

Partner Exit Slip relate to the first derivative? The second derivative?

Complete the Exit Slip with your partner on the sheet provided.

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