Absolute Extrema
1 hr 54 min 17 Examples
- What are Absolute Extrema? Relative Extrema? Extreme Value Theorem?
- Use the graph to identify the absolute and local extrema (Examples #1-2)
- Sketch the graph of the function given properties (Examples #3-4)
- Find the critical numbers of the polynomial function (Examples #5-6)
- Find the critical numbers when f’=0 or undefined (Examples #7-10)
- Steps for finding Absolute Extrema on a closed interval
- Locate the absolute extreme of the function on the closed interval (Examples #11-14)
- Locate the global extrema of transcendental functions (Examples #15-16)
- Find the absolute extrema of the piecewise function (Example #17)
Rolles Theorem
44 min 9 Examples
- What is the Intermediate Value Theorem? What is Rolle’s Theorem?
- If Rolle’s Theorem applies find all values of c that satisfy (Examples #1-2)
- Determine if Rolle’s Theorem applies and find all values of c (Examples #3-6)
- Give a reason for why Rolle’s Theorem does not apply (Examples #7-9)
Mean Value Theorem
42 min 8 Examples
- What is the Mean Value Theorem?
- Determine if Mean Value Theorem applies and if so find c (Examples #1-2)
- Apply MVT to find all values c that satisfy the conclusion (Examples #3-6)
- Does the Mean Value Theorem apply and if so find c (Example #7)
- Explain why there must be a value c such that f'(c)=-1 (Example #8)
First Derivative Test
1 hr 57 min 13 Examples
- Test for increasing or decreasing functions
- Given a graph identify the open intervals on which the function is increasing or decreasing (Examples #1-3)
- Steps for finding increasing or decreasing intervals (Examples #4-7)
- Overview of the First Derivative Test
- Use the first derivative test to find increasing or decreasing intervals and locate all relative extrema (Examples #8-10)
- Find increasing-decreasing intervals and local extrema using first derivative test (Examples #11-13)
Second Derivative Test
2 hr 20 min 15 Examples
- Test for Concavity and Points of Inflection
- Find the open intervals on which f is concave up or concave down (Examples #1-3)
- Determine the points of inflection and discuss concavity (Examples #4-6)
- What is the Second Derivative Test?
- Use the second derivative test to find relative extrema (Examples #7-9)
- Use the first and second derivative test to find local extrema (Examples #10-11)
- For the polynomial function find local extrema, increasing or decreasing intervals, points of inflection and concavity (Example #12)
- For the exponential function find local extrema, increasing or decreasing intervals, points of inflection and concavity (Example #13)
- For the logarithmic function find local extrema, increasing or decreasing intervals, points of inflection and concavity (Example #14)
- For the trigonometric function find local extrema, increasing or decreasing intervals, points of inflection and concavity (Example #15)
Curve Sketching
1 hr 53 min 6 Examples
- Summary of Curve Sketching Techniques
- Sketch and analyze the polynomial function (Example #1)
- Sketch and analyze the rational function (Example #2)
- Analyze and sketch the exponential curve (Example #3)
- Analyze and sketch the trigonometric curve (Example #4)
- Use curve sketching techniques to sketch the curve (Examples #5-6)
Derivative Graph
1 hr 18 min 16 Examples
- How to graph f’ given the graph of f (Examples #1-3)
- Given the graph of f(x) sketch the graph of f'(x) (Examples #4-10)
- How to read the derivative’s graph
- Use the graph of f’ to find properties of f(x) (Examples #11-12)
- Determine the interval where the graph is both increasing and concave up (Example #13)
- If f, f’, and f” are all positive which could be the graph of f? (Example #14)
- Given the graph of f” which could be the graph of f? (Example #15)
- f(x) is a twice differentiable function which of the following is true (Example #16)
Particle Motion
1 hr 42 min 5 Examples
- Particle Motion definitions, terminology, and theorems
- Find the initial position. When the particle is at rest? changing direction? (Example #1:a-e)
- When is the velocity increasing? When is the speed increasing (Example #1:f-h)
- Find the displacement and total distance (Example #1:i-j)
- When the object is at rest and moving left or right (Example #2:a-d)
- For what intervals is the velocity increasing and the speed increasing or decreasing (Example #2:e-g)
- Determine the displacement and total distance of the object (Example #2h)
- Given a graph of the velocity determine max speed, average acceleration, furthest right (Example #3:a-f)
- Given a table of select values of the velocity of a particle determine the following (Example #4:a-d)
- When is the distance increasing? Find the minimum value of the speed (Example #5:a-b)
Optimization
1 hr 32 min 7 Examples
- The three-steps for solving optimization problems
- Find the maximum area of a rectangle given perimeter constraints (Example #1)
- What dimension will produce a box of maximum volume (Example #2)
- What dimension require the least amount of fencing (Example #3)
- Find the dimension to so the enclosed area is maximized (Example #4)
- Find the dimensions of the page be so the least amount of paper is used (Example #5)
- Find the point(s) on the graph of the function closest to the given point (Example #6a-b)
- How should they set the airfare to maximize revenue (Example #7)
Demand Function
1 hr 20 min 9 Examples
- Find marginal profit (Example #1)
- Find Cost, Average Cost, Marginal Cost and Minimum Average Cost (Example #2)
- Maximize Profit (Example #3)
- Determine product level that will Maximize Profit (Example #4)
- Find the Demand Function (Example #5)
- Find Demand Function, Revenue Function and maximum rebate (Example #6)
- Maximize Revenue (Example #7)
- Find Cost, Average Cost, Marginal Cost and Minimum Average Cost (Example #8)
- Determine product level that will Maximize Profit (Example #9)
Elasticity of Demand
30 min 5 Examples
- Find the Elasticity and interpret your results (Examples #1-2)
- Find Elasticity given demand function and interpret results (Example #3)
- Find Elasticity. Will an increase in price increase revenue? (Example #4)
- Find Elasticity. Should a hotel raise it’s prices? (Example #5)
Chapter Test
4 hr 1 min 33 Examples
- 33 Challenging Practice Problems
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment