Chapter 4 Goal: Students Will Be Able to Use Different Methods of Derivatives to Analyze

AB Calculus

Chapter 4 Goal: Students will be able to use different methods of derivatives to analyze characteristics of various functions analytically including: the concavity of a function, the points of inflection, the direction, horizontal & vertical tangent lines and the critical values of those functions.

Ch./Obj. / Objective / Vocabulary / Lesson Plan
4.1
(1 day) / 4.1: Students will be able to calculate whether a function is differentiable based on it’s continuity and it’s derivative at a certain point. / Prior Vocabulary:
continuity, derivative, point
New Vocabulary:
differentiable, differentiability / 1.Spiral: find whether a function is continuous
2.New: check if a function has the same slope as another at a certain point
3.Assess: (Call Out)
4.Worksheet: Differentiable
4.2
(1 day) / 4.2: Students will be able to take the derivative of a function and use the derivative to find the horizontal tangent lines of that same function algebraically. / Prior Vocabulary:
Derivative, factoring, roots, solutions, zeros, tangent
New Vocabulary:
Horizontal tangent line / 1.Spiral: Find the point where a function has a certain slope
2.New: Set the derivative equal to zero to find the horizontal tangent lines
3.Assess: (Popcorn) Find the horizontal tangent lines
4.Worksheet: Horizontal tangent lines
4.3
(1 day) / 4.3: Students will be able to identify the location of a vertical tangent line given a function algebraically using the derivative of the function. / Prior Vocabulary:
Derivative, factoring, roots, solutions, zeros, tangent
New Vocabulary:
Vertical tangent line / 1.Spiral: Find the vertical asymptotes of a function algebraically
2.New: Find a vertical tangent line on a function algebraically
3.Assess: (Ind-Board) Find the vertical tangent line
4.Worksheet: Vertical Tangent Lines
Quiz
(1 day) / Quiz 4.1-4.3
4.4
(1 day) / 4.4: Students will be able to locate the horizontal tangent lines and use those values to aid in locating a functions direction algebraically; increasing or decreasing. / Prior Vocabulary:
Derivative, incdec, horizontal tangent
New Vocabulary:
None / 1.Spiral: Have the students locate the critical values of a function
2.New: Find the intervals where the function is inc or dec
3.Assess: (Ind-Board) Find the intervals of inc or dec
4.Worksheet: Increasing and decreasing functions

Ch./Obj. / Objective / Vocabulary / Lesson Plan
4.5
(1 day) / 4.5: Students will be able to locate and identify different types of critical values graphically, such as: absolute extrema, maximums and minimums. / Prior Vocabulary:
Critical values, maximum, minimum, endpoints
New Vocabulary:
Absolute extrema / 1.Spiral: Locate the max and mins of a function and review characteristics of derivatives
2.New: Identify the different types of critical values
3.Assess:(Group-board) Identify different critical values
1.Worksheet: first derivative test graphically
4.6
(1 day) / 4.6: Students will be able to locate and identify critical values algebraically and label these values as maximum, minimum and none. / Prior Vocabulary:
Critical values, maximum, minimum, endpoints
New Vocabulary:
None / 2.Spiral: Identify the intervals of incdec on a function
3.New: Use horizontal tangent lines and intervals to identify maximums and minimums
4.Assess: (Popcorn) number line scheme
1.Worksheet: First derivative test algebraically
4.7
(1 day) / 4.7: Students will be able to identify the absolute max or min value of a function algebraically. / Prior Vocabulary:
Critical values, maximum, minimum, endpoints
New Vocabulary:
Absolute extrema / 2.Spiral: On a graph locate the absolute max and min
3.New: Find the absolute max and min algebraically
4.Asses: (Call outs)
5.Worksheet: Absolute max & min algebraically
Quiz
(1 day) / Extrema Quiz / Prior Vocabulary:
New Vocabulary: / 1.Spiral:
2.New:
3.Assess:
4.Worksheet:
4.8
(1 day) / 4.8: Students will be able to locate a point of inflection and the intervals of concavity on a graph and algebraically to a function. / Prior Vocabulary:
Critical values, intervals, inc, dec, max, min
New Vocabulary:
point of inflection,concavity / 1.Spiral: Locate the Point of inflection on different graphs
2.New: Find the interval of concavity on function algebraically using the same method as the direction of the graph
3.Assess: (Ind-Board)
4.Worksheet: Point of Inflection & Concavity

Ch./Obj. / Objective / Vocabulary / Lesson Plan
4.9
(1 day) / 4.9: Students will be able to use the derivative of a graph find the characteristics of the original function, such as its direction and critical points to aid in sketching the original graph. / Prior Vocabulary:
Derivative, inc, dec, concavity, POI, CP, max, mins, second derivative / 1.Spiral: Find all the characteristics of a function given a graph of its derivative
2.New: Find the characteristics of the original function given a graph of its derivative then sketch the original
3.Assess: (Ind-Board)
4.Worksheet: f’(x) to f(x)
Quiz
(1 day) / Characteristics Quiz
4.10
(1 day) / 4.10: Students will be able to use the Mean value theorem of derivatives to find where a function’s instantaneous rate of change is equivalent to the function’s average rate of change over a given interval. / Prior Vocabulary:
Average ROC, Instantaneous ROC
New Vocabulary:
Mean Value Theorem / 1.Spiral: Find the instantaneous rate of change and the average rate of change of a function over some interval
2.New: Find where IROC=AROC
3.Assess: (Ind-Board)
4.Worksheet: MVT
4.11
(1 day) / 4.11: Students will be able to use Mean Value Theorem to understand the Rolle’s Theorem and Intermediate Value Theorem. / Prior Vocabulary:
Average ROC, Instantaneous ROC
New Vocabulary:
Mean Value Theorem / 1.Spiral: Find the MVT when the AROC is zero
2.New:Rolle’s Theorem & IVT
3.Assess: (Call Outs)
4.Worksheet:Rolle’s and IVT
4.12
(1 day) / 4.12: Students will be able to use the graph of the original function to determine the characteristics of the derivative and sketch a rough graph of the derivative. / Prior Vocabulary:
Derivative, inc, dec, concavity, POI, CP, max, mins, second derivative / 1.Spiral: Find all the characteristics of the derivative of the original function
2.New: Find all the characteristics of the derivative and then sketch the original
3.Assess:(Ind-Board & Mix and Match game)
4.Worksheet: f(x) to f’(x)
Test
(2 days) / Review & Chapter 4 Test

Personal Goal: Every Lesson should include a method of spiraling back & assessing students understanding before individual learning; as well as, clearly definingnew material that must be explained in detail to students.