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Absolute Extrema and the Extreme Value Theorem | Calculus 1 | MTH5101_Topic091
MTH5101 — Calculus 1
Other Lectures
Welcome to Calculus-1: Course Welcome and Introduction | Calculus 1 | MTH5101_Topic001Review of Sets | Calculus 1 | MTH5101_Topic002Real Numbers | Calculus 1 | MTH5101_Topic003Exponents and Scientific Notation | Calculus 1 | MTH5101_Topic004Radicals and Rational Exponents | Calculus 1 | MTH5101_Topic005Polynomials | Calculus 1 | MTH5101_Topic006Factoring of a Polynomial | Calculus 1 | MTH5101_Topic007Rational Expressions | Calculus 1 | MTH5101_Topic008Foundations of the Cartesian Plane and Plotting Points | Calculus 1 | MTH5101_Topic009Graphing with Intercepts, Distance, and Midpoint Techniques | Calculus 1 | MTH5101_Topic010Solving Linear and Quadratic Equations | Calculus 1 | MTH5101_Topic011Absolute Value Equations & Basic Inequalities | Calculus 1 | MTH5101_Topic012Absolute Value Inequalities | Calculus 1 | MTH5101_Topic013Function Definition and Notation | Calculus 1 | MTH5101_Topic014Domain and Range | Calculus 1 | MTH5101_Topic015Graphing Functions and Zeros | Calculus 1 | MTH5101_Topic016Combining Functions and Symmetry | Calculus 1 | MTH5101_Topic017Linear Functions and Slope | Calculus 1 | MTH5101_Topic018Polynomial Functions and Degree | Calculus 1 | MTH5101_Topic019Quadratic Functions and Roots | Calculus 1 | MTH5101_Topic020Rational Functions | Calculus 1 | MTH5101_Topic021Power and Root Functions | Calculus 1 | MTH5101_Topic022Algebraic vs Transcendental Functions | Calculus 1 | MTH5101_Topic023Piecewise-Defined Functions and Graphs | Calculus 1 | MTH5101_Topic024Angle Measure and Radians | Calculus 1 | MTH5101_Topic025Trigonometric Functions | Calculus 1 | MTH5101_Topic026Trigonometric Identities | Calculus 1 | MTH5101_Topic027Graphs and Periods of Trigonometric Functions | Calculus 1 | MTH5101_Topic028Inverse Functions | Calculus 1 | MTH5101_Topic029Finding Inverses, Graphing Inverses, and Restricted Domains | Calculus 1 | MTH5101_Topic030Inverse Trigonometric Functions | Calculus 1 | MTH5101_Topic031Exponential Functions | Calculus 1 | MTH5101_Topic032Laws of Exponents, and the Number e | Calculus 1 | MTH5101_Topic033Logarithmic Functions | Calculus 1 | MTH5101_Topic034Equations and Applications Involving Logarithms | Calculus 1 | MTH5101_Topic035Hyperbolic Functions | Calculus 1 | MTH5101_Topic036The Tangent Problem | Calculus 1 | MTH5101_Topic037Instantaneous Velocity and the Limit Process | Calculus 1 | MTH5101_Topic038What a Limit Means and Proper Notation | Calculus 1 | MTH5101_Topic039Estimating Limits Using Tables | Calculus 1 | MTH5101_Topic040Estimating Limits from Graphs and When Limits Fail | Calculus 1 | MTH5101_Topic041One-Sided Limits and their Relationship to Two-Sided Limits | Calculus 1 | MTH5101_Topic042Infinite Limits and Vertical Asymptotes | Calculus 1 | MTH5101_Topic043Basic Limit Laws | Calculus 1 | MTH5101_Topic044Applying the Limit Laws | Calculus 1 | MTH5101_Topic045Polynomial and Rational Function Limits | Calculus 1 | MTH5101_Topic046Factoring and Conjugate Techniques | Calculus 1 | MTH5101_Topic047Indeterminate (0/0) Form: Factor and Cancel | Calculus 1 | MTH5101_Topic048Conjugates for Radical Expressions | Calculus 1 | MTH5101_Topic049Simplifying Complex Fractions and Creative Algebra | Calculus 1 | MTH5101_Topic050Evaluating Two Sided Limits Algebraically | Calculus 1 | MTH5101_Topic051Limits of the Form K/0 and Infinite Behavior | Calculus 1 | MTH5101_Topic052Fundamental Trigonometric Limits and the Squeeze Theorem | Calculus 1 | MTH5101_Topic053Continuity at a Point: The Three Conditions | Calculus 1 | MTH5101_Topic054Types of Discontinuities and Intermediate Value Theorem | Calculus 1 | MTH5101_Topic055Solving for K to Ensure Continuity at x=a | Calculus 1 | MTH5101_Topic056Review of Limits & Continuity | Calculus 1 | MTH5101_Topic057Tangent Lines and Secant Lines | Calculus 1 | MTH5101_Topic058The Derivative as a Limit | Calculus 1 | MTH5101_Topic059Estimating and Calculating Derivatives | Calculus 1 | MTH5101_Topic060Velocity and Instantaneous Rate of Change | Calculus 1 | MTH5101_Topic061Defining the Derivative Function | Calculus 1 | MTH5101_Topic062Graphing Derivatives and Differentiability | Calculus 1 | MTH5101_Topic063Higher Order Derivatives | Calculus 1 | MTH5101_Topic064The Constant Rule | Calculus 1 | MTH5101_Topic065The Power Rule (Positive Integers) | Calculus 1 | MTH5101_Topic066Power Rule for Negative Exponents | Calculus 1 | MTH5101_Topic067The Constant Multiple Rule | Calculus 1 | MTH5101_Topic068The Sum and Difference Rules | Calculus 1 | MTH5101_Topic069Combining Rules for Polynomials and Tangent Lines | Calculus 1 | MTH5101_Topic070The Product Rule | Calculus 1 | MTH5101_Topic071Applying the Product Rule | Calculus 1 | MTH5101_Topic072The Quotient Rule | Calculus 1 | MTH5101_Topic073Combining Differentiation Rules | Calculus 1 | MTH5101_Topic074Equations of Tangent Line | Calculus 1 | MTH5101_Topic075Derivatives of sin x and cos x | Calculus 1 | MTH5101_Topic076Derivatives of tan x, cot x, sec x and cosec x | Calculus 1 | MTH5101_Topic077The Chain Rule | Calculus 1 | MTH5101_Topic078Chain Rule with Power Rule and Trigonometric Functions | Calculus 1 | MTH5101_Topic079Advanced Chain Rule Applications | Calculus 1 | MTH5101_Topic080Derivatives of Exponential Functions | Calculus 1 | MTH5101_Topic081Derivatives of Logarithmic Functions | Calculus 1 | MTH5101_Topic082Implicit Differentiation | Calculus 1 | MTH5101_Topic083Derivative of Inverse Trigonometric Functions | Calculus 1 | MTH5101_Topic084Equations of Tangent Line | Calculus 1 | MTH5101_Topic085Higher-order Derivatives Using Differentiation Rules | Calculus 1 | MTH5101_Topic086Amount of Change, and Average vs Instantaneous Rates | Calculus 1 | MTH5101_Topic087Application of Rate of Change: Motion Along a Line | Calculus 1 | MTH5101_Topic088Linear Approximations | Calculus 1 | MTH5101_Topic089Differentials and Error Analysis | Calculus 1 | MTH5101_Topic090Local Extrema, Critical Numbers and Fermat’s Theorem | Calculus 1 | MTH5101_Topic092Systematic Search for Critical Points | Calculus 1 | MTH5101_Topic093Locating Absolute Extrema on Closed Intervals | Calculus 1 | MTH5101_Topic094Increasing/Decreasing via the First Derivative | Calculus 1 | MTH5101_Topic095The First Derivative Test (Classifying Critical Points) | Calculus 1 | MTH5101_Topic096Mean Value Theorem (Rolle's Theorem → MVT) | Calculus 1 | MTH5101_Topic097MVT Consequences, Inequalities & Velocity | Calculus 1 | MTH5101_Topic098Concavity, and Point of Inflection (1) | Calculus 1 | MTH5101_Topic099Concavity, and Point of Inflection (2) | Calculus 1 | MTH5101_Topic100The Second Derivative Test (1) | Calculus 1 | MTH5101_Topic101The Second Derivative Test (2) | Calculus 1 | MTH5101_Topic102Determining Monotonicity and Extrema from Graphs | Calculus 1 | MTH5101_Topic103Applied Optimization (1) – Closed Intervals | Calculus 1 | MTH5101_Topic104Applied Optimization (2) - Closed Intervals | Calculus 1 | MTH5101_Topic105Related Rates | Calculus 1 | MTH5101_Topic106Limits at Infinity | Calculus 1 | MTH5101_Topic107End Behaviour of Functions | Calculus 1 | MTH5101_Topic108Graphing a Function Using Limits and Derivatives (1) | Calculus 1 | MTH5101_Topic109Graphing a Function Using Limits and Derivatives (2) | Calculus 1 | MTH5101_Topic110L’Hôpital’s Rule: When and How to Use | Calculus 1 | MTH5101_Topic111L’Hôpital’s Rule: Other Indeterminate Forms and the Log Trick | Calculus 1 | MTH5101_Topic112Introduction to Antiderivatives and Indefinite Integrals | Calculus 1 | MTH5101_Topic113Properties of Integrals and Initial-value Problems | Calculus 1 | MTH5101_Topic114Sigma (Summation) Notation: The Language of Long Sums | Calculus 1 | MTH5101_Topic115From Sums to Areas: Rectangular Approximations | Calculus 1 | MTH5101_Topic116Riemann Sums: Leading to the Exact Area | Calculus 1 | MTH5101_Topic117The Definite Integral: Definition, Notation, and Meaning | Calculus 1 | MTH5101_Topic118Building Riemann Sums, and Evaluating by Definition | Calculus 1 | MTH5101_Topic119Evaluating by Geometry (Exact Areas from Simple Shapes) | Calculus 1 | MTH5101_Topic120Evaluating Net Signed Area by Geometry | Calculus 1 | MTH5101_Topic121Evaluating Total Area by Geometry | Calculus 1 | MTH5101_Topic122Properties of the Definite Integral | Calculus 1 | MTH5101_Topic123Comparison Properties of Integrals | Calculus 1 | MTH5101_Topic124Average Value of a Function, and Mean Value Theorem for Integrals | Calculus 1 | MTH5101_Topic125Fundamental Theorem of Calculus Part I (Integrals & Antiderivatives) | Calculus 1 | MTH5101_Topic126Fundamental Theorem of Calculus Part I (Two Variable Limits of Integration) | MTH5101_Topic127Fundamental Theorem of Calculus Part II (Evaluation Theorem) | Calculus 1 | MTH5101_Topic128Evaluating Integrals by Formulas (Algebraic Functions) | Calculus 1 | MTH5101_Topic129Evaluating Integrals by Formulas (Transcendental Functions) | Calculus 1 | MTH5101_Topic130The Net Change Theorem | Calculus 1 | MTH5101_Topic131Applying the Net Change Theorem | Calculus 1 | MTH5101_Topic132Integrals of Even and Odd Functions with Symmetric Limits | Calculus 1 | MTH5101_Topic133Substitution Rule for Indefinite Integrals: Algebraic Functions | Calculus 1 | MTH5101_Topic134Substitution Rule for Indefinite Integrals: Transcendental Functions | Calculus 1 | MTH5101_Topic135Substitution Rule for Definite Integrals | Calculus 1 | MTH5101_Topic136Substitution Rule Strategy and Common Patterns | Calculus 1 | MTH5101_Topic137Integrals of Exponential Functions | Calculus 1 | MTH5101_Topic138Integrals of Exponential Functions Real-life Applications | Calculus 1 | MTH5101_Topic139Integrals of Logarithmic Functions | Calculus 1 | MTH5101_Topic140Integration by Parts | Calculus 1 | MTH5101_Topic141Applying Integration by Parts More Than Once | Calculus 1 | MTH5101_Topic142Integration by Parts for Definite Integrals | Calculus 1 | MTH5101_Topic143Area between Two Curves - (I) | Calculus 1 | MTH5101_Topic144Area between Two Curves - (II) | Calculus 1 | MTH5101_Topic145Areas for Intersections and Compound Regions | Calculus 1 | MTH5101_Topic146Arc Length of a Curve | Calculus 1 | MTH5101_Topic147Physical Applications: Mass and Density | Calculus 1 | MTH5101_Topic148Physical Applications: Work Done by a Force | Calculus 1 | MTH5101_Topic149Physical Applications: Springs and Hooke’s Law | Calculus 1 | MTH5101_Topic150