Section 2.2 Day 1 Basic Differentiation Rules and Rates of Change

Section 2.2 Day 1 Basic Differentiation Rules and Rates of Change AP Calculus AB Learning Targets Define & apply Constant Rule Define & apply Power Rule Define & apply the Constant Multiple Rule Define & apply Sum & Difference Rules

Define & apply derivatives of Sine & Cosine Determine the equation of a tangent line Find the horizontal tangents of a function Recognize & apply the relationship between a position function and velocity function Con stan t

R u le The derivative of a constant function is 0. Example: Example: What is the derivative of at 0 Why is this true? Remember, the derivative is just the slope. Thus, what is the slope of any constant function? Simply 0!

e l u R r e w Po Example: Example:

Example: You can check this rule with all of the work from section 2.1 and the visual of the graphs from section 2.1. Constant Multiple Rule Let be any constant. Then, Example: Example:

Sum & Difference Rules Example: 1. 2. Example: Example:

Deri vativ Sine es o f & Co sine Example 1: Tangent Line Write the equation of the tangent line for at the point

1. Need a point: 2. Need a slope: 3. Put into point-slope form: Example 2: Tangent Line Write the equation of the tangent line for at the point 1. Need a point: 2. Need a slope:

3. Put in point-slope form: Example 3: Horizontal Tangents Does the curve have any horizontal tangents? If so, where? 1. Horizontal tangents means the slope of the horizontal is 0. 2. Need slope function:

3. Set it equal to 0 to find x values: 4. Thus, it occurs at Relationship between Position & Velocity Lets take a look at a function that represents the position of an object. What are the units of the slope of the function? Thus, the derivative of the position function is the velocity function.

Example 4: Position & Velocity pg113 Ex 9 If a billiard ball is dropped from a height of 100ft, its height, at time is given by the position function where is measured in feet and in seconds. A) Find the average velocity over the interval B) What is the velocity of the billiard ball at 4 seconds?

Example 4: Position & Velocity pg113 Ex 9 If a billiard ball is dropped from a height of 100ft, its height, at time is given by the position function where is measured in feet and in seconds. A) Find the average velocity over the interval This is AROC:

Example 4: Position & Velocity pg113 Ex 9 If a billiard ball is dropped from a height of 100ft, its height, at time is given by the position function where is measured in feet and in seconds. B) What is the velocity of the billiard ball at 4 seconds? This is IROC:

Exit Ticket for Feedback 1. Write the equation of the tangent line of at 2. A particles position function is determined by . What is the particles velocity at ?