منصة فنار التعليمية

الرياضيات - الثاني عشر المتقدم (باللغة الانكليزية) - الفصل الثاني

منصة فنار التعليمية

4.3 Maximum and Minimum Values

Maximum and Minimum Values 10:39

A Function with No Absolute Maximum or Minimum 03:34

A Function with a Zero Derivative at a Local
Maximum 04:36

A Horizontal Tangent at a Point That Is Not a
Local Extremum 03:52

A Vertical Tangent at a Point That Is Not a Local
Extremum 04:8

Finding Critical Numbers of a Rational Function 05:47

Finding Absolute Extrema on a Closed Interval 06:29

Finding Extrema for a Function with Fractional
Exponents 04:10

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4.4 Increasing and Decreasing Functions

Increasing and Decreasing Functions 09:7

Finding Local Extrema Using the First Derivative
Test 09:10

Finding Local Extrema of a Function with
Fractional Exponents 08:53

Finding Local Extrema Approximately 05:52

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4.5 Concavity and the Second Derivative Test

Concavity and the Second Derivative Test 02:54

Determining Concavity 04:1

Determining Concavity and Locating Inflection
Points 06:7

A Graph with No Inflection Points 02:50

Using the Second Derivative Test to Find Extrema 06:36

Functions for Which the Second Derivative Test Is
Inconclusive 05:10

Drawing a Graph of a Rational Function 07:31

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4.6 Overview of Curve Sketching

Overview of Curve Sketching 08:33

Drawing a Graph of a Rational Function 23:20

A Graph with Two Vertical Asymptotes 16:57

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4.7 Optimization

Optimization 03:45

Constructing a Rectangular Garden of Maximum Area 05:27

Constructing a Box of Maximum Volume 08:22

Finding the Closest Point on a Parabola 05:56

Designing a Soda Can Using a Minimum Amount of
Material 08:12

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4.8 Related Rates

Related Rates 09:17

A Sliding Ladder 05:29

Another Related Rates Problem 03:22

Estimating a Rate of Change in Economics 03:9

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4.9 Rates of Change in Economics and the Sciences

Rates of Change in Economics and the Sciences 06:9

Minimizing the Average Cost of Producing a
Commercial Product 08:5

Computing Elasticity of Demand and Changes in
Revenue 08:37

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5.1 Antiderivatives

Antiderivatives 07:43

An Indefinite Integral 05:59

Evaluating an Indefinite Integral 02:54

Using the Power Rule 01:49

The Power Rule with a Negative Exponent 03:13

The Power Rule with a Fractional Exponent 06:7

An Indefinite Integral of a Sum 07:51

An Indefinite Integral of a Difference 02:53

The Derivative of the Log of an Absolute Value 02:16

Corollary 02:3

The Indefinite Integral of a Fraction of the Form
F'x(x) over f(x) 01:43

Identifying Integrals That We Cannot Yet Evaluate 09:19

Finding the Position of a Falling Object Given Its
Acceleration 05:26

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5.2 Sums and Sigma Notation

Sums and Sigma Notation 04:19

Summation Notation for a Sum Involving Odd
Integers 04:3

Computing Sums Given in Summation Notation 04:33

Computing Sums Using Theorems 2.1 and 2.2 11:23

Computing a Sum of Function Values 04:48

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5.3 Area

Area 08:11

Computing the Area Exactly 07:18

Estimating the Area Under a Curve 02:53

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5.4 The Definite Integral

The Definite Integral 07:39

Relating Definite Integrals to Signed Area 06:45

An Integral with a Discontinuous Integrand 02:50

Estimating the Value of an Integral 02:28

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5.5 The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus 05:9

Computing a Definite Integral Exactly 03:27

Using the Fundamental Theorem to Compute Areas 02:8

A Definite Integral Involving an Exponential
Function 02:46

A Definite Integral Involving a Logarithm 03:14

A Definite Integral with a Variable Upper Limit 02:24

A Definite Integral with a Variable Upper Limit 06:19

Using the Chain Rule and the Fundamental Theorem,
Part II 01:51

An Integral with Variable Upper and Lower Limits 05:28

Computing the Distance Fallen by an Object 03:25

Rate of Change and Total Change of Volume of a
Tank 02:51

Finding a Tangent Line for a Function Defined as
an Integral 05:26

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5.6 Integration by Substitution

Integration by Substitution 05:39

Finding an Antiderivative by Trial and Error 04:47

Using Substitution to Evaluate an Integral 04:18

Using Substitution A Power Function Inside 03:46

Using Substitution A Trigonometric Function Inside
a Power 04:11

Using Substitution A Root Function Inside a Sine 03:2

Substitution Where the Numerator Is the Derivative
of the Denominator 03:53

An Antiderivative for the Tangent Function 05:37

A Substitution for an Inverse Tangent 03:24

A Substitution That Lets You Expand the Integrand 04:46

Using Substitution in a Definite Integral 04:3

Substitution in a Definite Integral 02:28

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