WHAT YOU SHOULD HAVE ON YOUR DESK…

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Presentation transcript:

WHAT YOU SHOULD HAVE ON YOUR DESK… Unit 3 Test Curve Sketching packet Curve Sketching unit plan (blue) Graphs for notes today (stapled together but you need to cut out) Orange chart (also for notes today) WHAT YOU NEED TO BE DOING… Get our your Unit 3 review HW & unit plan so you can show me that you did at least 40 problems Add HW points so we can figure out your Unit 3 HW grade Cut out graphs on stapled packet

Keeper 21 Honors Calculus Curve Sketching Keeper 21 Honors Calculus

When is a graph differentiable A graph is differentiable anywhere EXCEPT where there is the following : Cusp Corner Vertical Tangent Discontinuity Removable Infinite Jump

State the x values where 𝑓 is not differentiable and the reason

State the x values where 𝑓 is not differentiable and the reason

Critical points, Concavity & inflection points Maximum Critical Points – the graph’s turning points or the Local Max (peaks) & Local Mins (valleys) Inflection Points – a point on a graph where it changes concavity. 1 side is concave down & 1 side is concave up Minimum

Relationship Between 𝑓, 𝑓 ′ , 𝑓′′ -Cusp -Corner -Discontinuity -Removable -Infinite -jump -Vertical Tangent DNE Local max, local min (local extrema), horizontal tangent On the x-axis 𝑓 increasing Positive (Above the x-axis) 𝑓 decreasing Negative (Below the x-axis) 𝑓 concave up Increasing 𝑓 concave down Decreasing Points of Inflections Local Extrema Change Signs

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔(𝑥) 1.

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔 𝑥 2.

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔(𝑥) 3.

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔 𝑥 4.

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔 𝑥 5.

What can we say about 𝑔, 𝑔 ′ , 𝑔′′ for each segment of the graph 𝑦=𝑔 𝑥 6.

1. Graph the First Derivative

2. Graph the First Derivative

3. Graph the First Derivative

4. Graph the First Derivative

5. Graph the First Derivative

6. Graph the First Derivative

7. Graph the F’(x) and f”(x)

8. Graph the F’(x) and f”(x)

Graph the First Derivative

Graph the First Derivative