Application of Derivatives

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Application of Derivatives

• Dr. Ching I Chen

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4.1 Extreme Values of Functions (1) Absolute
(Global) Extreme Values
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4.1 Extreme Values of Functions (2) Absolute
(Global) Extreme Values (Example 1)
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4.1 Extreme Values of Functions (3) Absolute
(Global) Extreme Values (Example 2-a)
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4.1 Extreme Values of Functions (4) Absolute
(Global) Extreme Values (Example 2-b)
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4.1 Extreme Values of Functions (5) Absolute
(Global) Extreme Values (Example 2-c)
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4.1 Extreme Values of Functions(6, Example 2-d)
Absolute (Global) Extreme Values
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4.1 Extreme Values of Functions (7) Absolute
(Global) Extreme Values (Theorem 1)
Maximum and minimum at interior points
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4.1 Extreme Values of Functions (8) Absolute
(Global) Extreme Values (Theorem 1)
Maximum and minimum at endpoints
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4.1 Extreme Values of Functions (9) Absolute
(Global) Extreme Values (Theorem 1)
Maximum at interior point, minimum at endpoint
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4.1 Extreme Values of Functions (10) Absolute
(Global) Extreme Values (Theorem 1)
Minimum at interior point, maximum at endpoint
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4.1 Extreme Values of Functions (11) Local
(Relative) Extreme Values
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4.1 Extreme Values of Functions (12) Local
(Relative) Extreme Values
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4.1 Extreme Values of Functions (13) Finding
Extreme Values (Theorem 2)
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4.1 Extreme Values of Functions (14) Finding
Extreme Values
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4.1 Extreme Values of Functions (15) Finding
Extreme Values (Example 3-1)
Absolute maximum value of about 2 at x 3 and
absolute minimum value of 0 at x 0
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4.1 Extreme Values of Functions (16) Finding
Extreme Values (Example 3-2)
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4.1 Extreme Values of Functions (17) Finding
Extreme Values (Example 4)
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4.1 Extreme Values of Functions (18) Finding
Extreme Values (Example 5-1)
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4.1 Extreme Values of Functions (19) Finding
Extreme Values (Example 5-2)
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4.1 Extreme Values of Functions (20) Finding
Extreme Values (Example 6)
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4.1 Extreme Values of Functions (21) Finding
Extreme Values (Exploration 1)
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4.1 Extreme Values of Functions (22) Finding
Extreme Values (Exploration 1-2)
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4.1 Extreme Values of Functions (23)
Exercise 1 , 4, 7, 10, 13, 16, 19, 22, 25, 28,
31, 34, 37, 40, 43
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4.2 Mean Value Theorem (1) Mean Value Theorem
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4.2 Mean Value Theorem (2) Mean Value Theorem
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4.2 Mean Value Theorem (3) Mean Value Theorem
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4.2 Mean Value Theorem (4, Example 1) Mean Value
Theorem
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4.2 Mean Value Theorem (5, Example 2) Mean Value
Theorem
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4.2 Mean Value Theorem (6, Example 3) Physical
Interpretation
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4.2 Mean Value Theorem (7) Increasing and
Decreasing Functions
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4.2 Mean Value Theorem (8, Example 4) Increasing
and Decreasing Functions
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4.2 Mean Value Theorem (9, Example 5) Increasing
and Decreasing Functions
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4.2 Mean Value Theorem (10) Other Consequences
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4.2 Mean Value Theorem (11, Example 6) Other
Consequences
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4.2 Mean Value Theorem (12) Other Consequences
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4.2 Mean Value Theorem (13, Example 7) Other
Consequences
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4.3 Connecting f ? and f ? with the Graph of f
(1) First Derivative Test for Local Extrema
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4.3 Connecting f ? and f ? with the Graph of f
(2) First Derivative Test for Local Extrema
(Theorem 4)
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4.3 Connecting f ? and f ? with the Graph of f
(3) First Derivative Test for Local Extrema
(Theorem 4)
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4.3 Connecting f ? and f ? with the Graph of f
(4) First Derivative Test for Local Extrema
(Theorem 4)
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4.3 Connecting f ? and f ? with the Graph of f
(5) First Derivative Test for Local Extrema
(Theorem 4)
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4.3 Connecting f ? and f ? with the Graph of f
(6) First Derivative Test for Local Extrema
(Theorem 4)
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4.3 Connecting f ? and f ? with the Graph of f
(7) First Derivative Test for Local Extrema
(Example 1)
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4.3 Connecting f ? and f ? with the Graph of f
(8) First Derivative Test for Local Extrema
(Example 2)
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4.3 Connecting f ? and f ? with the Graph of f
(9) Concavity
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4.3 Connecting f ? and f ? with the Graph of f
(10) Concavity
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4.3 Connecting f ? and f ? with the Graph of f
(11) Concavity (Example 3)
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4.3 Connecting f ? and f ? with the Graph of f
(12) Concavity (Example 4)
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4.3 Connecting f ? and f ? with the Graph of f
(13)Points of Inflection
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4.3 Connecting f ? and f ? with the Graph of f
(14) Points of Inflection (Example 5-1)
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4.3 Connecting f ? and f ? with the Graph of f
(15) Points of Inflection (Example 5-2)
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4.3 Connecting f ? and f ? with the Graph of f
(16) Points of Inflection (Example 5-3)
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4.3 Connecting f ? and f ? with the Graph of f
(17) Points of Inflection (Example 6)
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4.3 Connecting f ? and f ? with the Graph of f
(18) Points of Inflection (Example 6)
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4.3 Connecting f ? and f ? with the Graph of f
(19) Second Derivative Test for Local Extrema
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4.3 Connecting f ? and f ? with the Graph of f
(20) Second Derivative Test for Local Extrema
(Ex. 7)
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4.3 Connecting f ? and f ? with the Graph of f
(21) Second Derivative Test for Local Extrema
(Ex. 8)
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4.3 Connecting f ? and f ? with the Graph of f
(22) Second Derivative Test for Local Extrema
(Ex. 8-a,b)
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4.3 Connecting f ? and f ? with the Graph of f
(23) Second Derivative Test for Local Extrema
(Ex. 8-c,d)
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4.3 Connecting f ? and f ? with the Graph of f
(24) Learning about Function From Derivatives
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4.3 Connecting f ? and f ? with the Graph of f
(25) Learning about Function From Derivatives
(Explo. 2)
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4.4 Modeling and Optimization (1, Example 1)
Example from Business and Industry
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4.4 Modeling and Optimization (2, Example 2)
Example from Business and Industry
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4.4 Modeling and Optimization (3, Example 3)
Example from Mathematics
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4.4 Modeling and Optimization (4, Example 4)
Example from Mathematics
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4.4 Modeling and Optimization (5) Example from
Mathematics(Exploration 1)
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4.4 Modeling and Optimization (6) Example from
Mathematics (Exploration 1-1)
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4.4 Modeling and Optimization (7) Example from
Mathematics (Exploration 1-2)
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4.4 Modeling and Optimization (8) Example from
Mathematics (Exploration 1-3)
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4.4 Modeling and Optimization (9) Example from
Mathematics (Exploration 1-4)
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4.4 Modeling and Optimization (10) Example from
Mathematics (Exploration 1-5)
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4.4 Modeling and Optimization (11) Example from
Economics
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4.4 Modeling and Optimization (12) Example from
Economics
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4.4 Modeling and Optimization (13, Example 5)
Example from Economics
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4.4 Modeling and Optimization (14, Example 6)
Example from Economics
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4.5 Linearization and Newtons Method (1) Linear
Approximation (Exploration 1-1,2)
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4.5 Linearization and Newtons Method (2) Linear
Approximation (Exploration 1-3)
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4.5 Linearization and Newtons Method (3) Linear
Approximation
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4.5 Linearization and Newtons Method (4) Linear
Approximation (Example 1)
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4.5 Linearization and Newtons Method (5) Linear
Approximation (Example 2)
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4.5 Linearization and Newtons Method (6) Linear
Approximation (Example 3)
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4.5 Linearization and Newtons Method (7) Linear
Approximation (Example 4)
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4.5 Linearization and Newtons Method (8)
Newtons Method
Newtons method is a numerical technique for
approximating a zero of a function of with zeros
of its linearizations. Under favorable
circumstances, The zeros of the linearizations
converge rapidly to an accurate approximation.
Many calculators use the method because it
applies to a wide range of functions and usually
gets results in only a few steps.
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4.5 Linearization and Newtons Method (9)
Newtons Method
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4.5 Linearization and Newtons Method (10)
Newtons Method
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4.5 Linearization and Newtons Method (11)
Newtons Method (Example 5)
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4.5 Linearization and Newtons Method (12)
Newtons Method
Fig 4.43
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4.5 Linearization and Newtons Method (13)
Newtons Method
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4.5 Linearization and Newtons Method (14)
Differentials
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4.5 Linearization and Newtons Method (15)
Differentials (Example 6)
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4.5 Linearization and Newtons Method (16)
Differentials (Example 7)
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4.5 Linearization and Newtons Method (17)
Estimating Change with Differentials
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4.5 Linearization and Newtons Method (18)
Estimating Change with Differentials
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4.5 Linearization and Newtons Method (19)
Estimating Change with Differentials (Example 8)
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4.5 Linearization and Newtons Method (20)
Absolute, Relative, and Percentage Change
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4.5 Linearization and Newtons Method (21)
Absolute, Relative, and Percentage Change (Ex. 9)
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4.5 Linearization and Newtons Method (22)
Absolute, Relative, and Percentage Change (Ex.
10)
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4.5 Linearization and Newtons Method (23)
Absolute, Relative, and Percentage Change (Ex.
11)
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4.5 Linearization and Newtons Method (24)
Absolute, Relative, and Percentage Change (Ex.
12)
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4.5 Linearization and Newtons Method (25)
Sensitivity to Change (Ex. 13)
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4.6 Related Rates (1) Related Rate Equations
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4.6 Related Rates (2, Example 1) Related Rate
Equations
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4.6 Related Rates (3, Example 2-1) Solution
Strategy
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4.6 Related Rates (3, Example 2-2) Solution
Strategy
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4.6 Related Rates (4, Example 2-3) Solution
Strategy
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4.6 Related Rates (5, Example 2-4) Solution
Strategy
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4.6 Related Rates (6, Example 2-5) Solution
Strategy
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4.6 Related Rates (7) Solution Strategy
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4.6 Related Rates (8) Solution Strategy
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4.6 Related Rates (8, Example 3-1) Related Rate
Equations
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4.6 Related Rates (10, Example 3-2) Related Rate
Equations
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4.6 Related Rates (11, Example 3-3) Solution
Strategy
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4.6 Related Rates (12, Example 3-4) Solution
Strategy
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4.6 Related Rates (13, Example 3-5) Solution
Strategy
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4.6 Related Rates (14, Example 4-1) Related Rate
Equations
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4.6 Related Rates (15, Example 4-2) Related Rate
Equations
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4.6 Related Rates (16, Example 4-3) Solution
Strategy
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4.6 Related Rates (17, Example 4-4) Solution
Strategy
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4.6 Related Rates (18, Example 4-5) Solution
Strategy